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Theorem on holomorphic functions
In complex analysis, the open mapping theorem states that if U {\displaystyle U} is a domain of the complex plane C {\displaystyle \mathbb {C} } and f
Open mapping theorem (complex analysis)
Open_mapping_theorem_(complex_analysis)
Condition for a linear operator to be open
In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem (named after Stefan Banach and Juliusz
Open mapping theorem (functional analysis)
Open_mapping_theorem_(functional_analysis)
Index of articles associated with the same name
is an open mapping Open mapping theorem (complex analysis), states that a non-constant holomorphic function on a connected open set in the complex plane
Open_mapping_theorem
Mathematical theorem
In complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number
Riemann_mapping_theorem
Branch of mathematics studying functions of a complex variable
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions
Complex_analysis
Theorem in complex analysis
In complex analysis, Liouville's theorem states that every bounded entire function must be constant. That is, every holomorphic function f {\displaystyle
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
Mathematical function that preserves angles
it is periodic. The Riemann mapping theorem, one of the profound results of complex analysis, states that any non-empty open simply connected proper subset
Conformal_map
theorem (complex analysis) Nachbin's theorem(complex analysis) Open mapping theorem (complex analysis) Ostrowski–Hadamard gap theorem (complex analysis) Phragmén–Lindelöf
List_of_theorems
Limit of roots of sequence of functions
In mathematics and in particular the field of complex analysis, Hurwitz's theorem is a theorem associating the zeroes of a sequence of holomorphic, compact
Hurwitz's theorem (complex analysis)
Hurwitz's_theorem_(complex_analysis)
Theorem in complex analysis
Carathéodory's theorem is a theorem in complex analysis, named after Constantin Carathéodory, which extends the Riemann mapping theorem. The theorem, published
Carathéodory's theorem (conformal mapping)
Carathéodory's_theorem_(conformal_mapping)
This is a glossary of concepts and results in real analysis and complex analysis in mathematics. In particular, it includes those in measure theory (as
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
Theorem about the range of an analytic function
In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after
Picard_theorem
Concept of complex analysis
In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions
Residue_theorem
Theorem in complex analysis
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard
Cauchy's_integral_theorem
Homeomorphism between plane domains
In mathematical complex analysis, a quasiconformal mapping is a (weakly differentiable) homeomorphism between plane domains which to first order takes
Quasiconformal_mapping
Area of mathematics
Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered
Functional_analysis
Theorem about zeros of holomorphic functions
Riemann mapping theorem – Mathematical theorem Sturm's theorem – Counting polynomial roots in an interval Needham, Tristan (2023). Visual Complex Analysis. Oxford
Rouché's_theorem
Mathematical theorem in complex analysis
as a special case of the open mapping theorem, which states that a nonconstant holomorphic function maps open sets to open sets: If | f | {\displaystyle
Maximum_modulus_principle
Type of vector space in math
spectral methods is the spectral mapping theorem, which allows one to apply to a self-adjoint operator T any continuous complex function f defined on the spectrum
Hilbert_space
In mathematics, the analytic Fredholm theorem is a result concerning the existence of bounded inverses for a family of bounded linear operators on a Hilbert
Analytic_Fredholm_theorem
Integral criterion for holomorphy
In complex analysis, a branch of mathematics, Morera's theorem, named after Giacinto Morera, gives a criterion for proving that a function is holomorphic
Morera's_theorem
Two theorems about families of holomorphic functions
In complex analysis, an area of mathematics, Montel's theorem refers to one of two theorems about families of holomorphic functions. These are named after
Montel's_theorem
Complex Analysis, Fixed-points and Iterations of Holomorphic Mappings
Denjoy–Wolff theorem is a theorem in complex analysis and dynamical systems concerning fixed points and iterations of holomorphic mappings of the unit
Denjoy–Wolff_theorem
In mathematics, the Carathéodory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin
Carathéodory_kernel_theorem
Mathematical theorem
In complex analysis, a branch of mathematics, Bloch's theorem describes the behaviour of holomorphic functions defined on the unit disk. It gives a lower
Bloch's theorem (complex analysis)
Bloch's_theorem_(complex_analysis)
Statement in complex analysis
classical Schwarz lemma is a result in complex analysis typically viewed to be about holomorphic functions from the open unit disk D := { z ∈ C : | z | < 1
Schwarz_lemma
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f
Brouwer_fixed-point_theorem
Theorem in complex analysis
In complex analysis, the argument principle (or Cauchy's argument principle) is a theorem relating the difference between the number of zeros and poles
Argument_principle
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating that
Mean_value_theorem
Attribute of a mathematical function
In mathematics, more specifically complex analysis, the residue of a function at a point of its domain is a complex number proportional to the contour
Residue_(complex_analysis)
Objects that generalize functions
condition for extending F# to distributions is that F be an open mapping. The inverse function theorem ensures that a submersion satisfies this condition. If
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
conformal mappings, the area theorem gives an inequality satisfied by the power series coefficients of certain conformal mappings. The theorem is called
Area theorem (conformal mapping)
Area_theorem_(conformal_mapping)
Mathematics of real numbers and real functions
bound that is smaller than all of the others. Most of the theorems that are proved in real analysis rely on completeness in one way or another. Some examples
Real_analysis
Type of function in mathematics
mathematical analysis, an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex function
Analytic_function
fixed point theorem is a result in geometric function theory giving sufficient conditions for a holomorphic mapping of an open domain in a complex Banach space
Earle–Hamilton fixed-point theorem
Earle–Hamilton_fixed-point_theorem
Type of mathematical functions
establishment of the inverse function theorem, the following mapping can be defined. For the domain U, V of the n-dimensional complex space C n {\displaystyle \mathbb
Function of several complex variables
Function_of_several_complex_variables
Way to divide polygon into smaller parts
proofs in higher-dimensional mathematical analysis such as for the Bolzano–Weierstrass theorem and Heine–Borel theorem. A finite subdivision rule R {\displaystyle
Finite_subdivision_rule
Theorem
radius of convergence is positive). One of the most important theorems of complex analysis is that holomorphic functions are analytic and vice versa. (A
Analyticity of holomorphic functions
Analyticity_of_holomorphic_functions
Simply connected Riemann surface is equivalent to an open disk, complex plane, or sphere
disk, the complex plane, or the Riemann sphere. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of
Uniformization_theorem
Theorem in mathematics
In mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that
Inverse_function_theorem
On topological spaces where the intersection of countably many dense open sets is dense
L^{2}(\mathbb {R} ^{n})} . In functional analysis, BCT1 can be used to prove the open mapping theorem, the closed graph theorem and the uniform boundedness principle
Baire_category_theorem
Complex-differentiable (mathematical) function
That all holomorphic functions are complex analytic functions, and vice versa, is a major theorem in complex analysis. Holomorphic functions are also sometimes
Holomorphic_function
Theorem in calculus relating line and double integrals
In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R
Green's_theorem
Concept in mathematics
One way to prove this theorem is to deduce it from the properties of the action of the mapping class group on the pants complex: the stabiliser of a vertex
Mapping class group of a surface
Mapping_class_group_of_a_surface
One-dimensional complex manifold
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied
Riemann_surface
Mathematical concept
Statement in complex analysis; formerly the Bieberbach conjecture Koebe quarter theorem – Statement in complex analysis Riemann mapping theorem – Mathematical
Univalent_function
Multivariate functions can be written using univariate functions and summing
In real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous
Kolmogorov–Arnold representation theorem
Kolmogorov–Arnold_representation_theorem
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x
Implicit_function_theorem
Bound on eigenvalues
principle of complex analysis requires no eigenvalue continuity of any kind. For a brief discussion and clarification, see. The Gershgorin circle theorem is useful
Gershgorin_circle_theorem
Provides integral formulas for all derivatives of a holomorphic function
result that does not hold in real analysis. Let U ⊂ C {\displaystyle U\subset \mathbb {C} } be an open subset of the complex plane C {\displaystyle \mathbb
Cauchy's_integral_formula
Theorem stating that pointwise boundedness implies uniform boundedness
Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered
Uniform_boundedness_principle
Bijective holomorphic function with a holomorphic inverse
simply connected open set other than the whole complex plane is biholomorphic to the unit disc (this is the Riemann mapping theorem). The situation is
Biholomorphism
Concept in complex analysis
In complex analysis, a branch of mathematics, the antiderivative, or primitive, of a complex-valued function g is a function whose complex derivative
Antiderivative (complex analysis)
Antiderivative_(complex_analysis)
list of articles that are considered real analysis topics. See also: glossary of real and complex analysis. Limit of a sequence Subsequential limit –
List_of_real_analysis_topics
Concept in complex analysis
In complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. It is the simplest
Zeros_and_poles
Number with a real and an imaginary part
fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number
Complex_number
as of September 2022[update]. The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic
List_of_conjectures
theorem Open mapping theorem (functional analysis) Product topology Riemann integral Time hierarchy theorem Deterministic time hierarchy theorem Furstenberg's
List_of_mathematical_proofs
Statement in complex analysis; formerly the Bieberbach conjecture
In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order
De_Branges's_theorem
Theorem in complex analysis
In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application
Borel–Carathéodory_theorem
Characterization of surjectivity
importance of this theorem is related to the open mapping theorem, which states that a continuous linear surjection between Fréchet spaces is an open map. Often
Surjection_of_Fréchet_spaces
Generalization of the concept of directional derivative
analogous to the result from basic complex analysis that a function is analytic if it is complex differentiable in an open set, and is a fundamental result
Gateaux_derivative
Number of times a curve wraps around a point in the plane
important role throughout complex analysis (cf. the statement of the residue theorem). In the context of complex analysis, the winding number of a closed
Winding_number
Branch of mathematics
Complex dynamics, or holomorphic dynamics, is the study of dynamical systems obtained by iterating a complex analytic mapping. This article focuses on
Complex_dynamics
Functions that send open (resp. closed) subsets to open (resp. closed) subsets
In complex analysis, the identically named open mapping theorem states that every non-constant holomorphic function defined on a connected open subset
Open_and_closed_maps
Theorem in topology
(1924). Due to the importance of the Jordan curve theorem in low-dimensional topology and complex analysis, it received much attention from prominent mathematicians
Jordan_curve_theorem
Representation theory
In mathematics, the Plancherel theorem for spherical functions is an important result in the representation theory of semisimple Lie groups, due in its
Plancherel theorem for spherical functions
Plancherel_theorem_for_spherical_functions
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
Using the Jordan normal form, direct calculation gives a spectral mapping theorem for the polynomial functional calculus: Let A be an n × n matrix with
Jordan_normal_form
Functions in mathematics
principle; a theorem of removal of singularities as well as a Liouville theorem holds for them in analogy to the corresponding theorems in complex functions
Harmonic_function
Mathematical theorem
Ωn containing the closure of Ωn + 1. By the Riemann mapping theorem there is a conformal mapping fn of Ωn onto Ω, normalised to fix a given point in Ω
Farrell–Markushevich_theorem
category theorem Open mapping theorem (functional analysis) Closed graph theorem Uniform boundedness principle Arzelà–Ascoli theorem Banach–Alaoglu theorem Measure
List of functional analysis topics
List_of_functional_analysis_topics
German mathematician (1826–1866)
this area are numerous. The famous Riemann mapping theorem says that a simply connected domain in the complex plane is "biholomorphically equivalent" (i
Bernhard_Riemann
Study of space and shapes locally given by a convergent power series
analytic functions. A fundamental result in the theory is the Riemann mapping theorem. The following are some of the most important topics in geometric function
Geometric_function_theory
unit group of A. open The open mapping theorem says a surjective continuous linear operator between Banach spaces is an open mapping. orthonormal 1. A
Glossary of functional analysis
Glossary_of_functional_analysis
Characteristic property of holomorphic functions
addresses these kinds of questions. List of complex analysis topics Cauchy integral theorem Morera's theorem Wirtinger derivatives d'Alembert, Jean (1752)
Cauchy–Riemann_equations
Geometric representation of the complex numbers
is sometimes called the Argand plane or Gauss plane. In complex analysis, the complex numbers are customarily represented by the symbol z, which can be
Complex_plane
Space which has no holes through it
important in complex analysis because of the following facts: Cauchy's integral theorem states that if U {\displaystyle U} is a simply connected open subset
Simply_connected_space
Degree of differentiability of a function or map
Discontinuity – Mathematical analysis of discontinuous pointsPages displaying short descriptions of redirect targets Hadamard's lemma – TheoremPages displaying short
Smoothness
contraction mapping and a non-expansion mapping (or vice versa) is a contraction mapping. If T {\displaystyle T} is not a contraction mapping on its entire
Convergence_proof_techniques
Canadian–American mathematician
Pennsylvania) was a Canadian–American mathematician, specializing in complex analysis. James A. Jenkins was born 23 September 1923 in Toronto, Ontario and
James_Allister_Jenkins
Branch of mathematics
by sums of trigonometric functions or more conveniently, complex exponentials. Fourier analysis grew from the study of Fourier series, and is named after
Fourier_analysis
Particular kind of algebraic structure
functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A {\displaystyle A} over the real or complex numbers (or
Banach_algebra
Mathematics glossary
via a ring homomorphism L → R mapping ƒ to g. According to Quillen's theorem, it is also the coefficient ring of the complex bordism MU. The Spec of L is
Glossary of algebraic topology
Glossary_of_algebraic_topology
Construction in functional analysis, useful to solve differential equations
its inverse is bounded; this follows directly from the open mapping theorem of functional analysis. So, λ is in the spectrum of T if and only if T − λ is
Decomposition of spectrum (functional analysis)
Decomposition_of_spectrum_(functional_analysis)
Statement on solutions to ordinary differential equations
on R {\displaystyle R} if it fulfills the condition of the theorem. Assume that the mapping f {\displaystyle f} satisfies the Carathéodory conditions on
Carathéodory's existence theorem
Carathéodory's_existence_theorem
Two-dimensional manifold
metric or a complex structure, that connects them to other disciplines within mathematics, such as differential geometry and complex analysis. The various
Surface_(topology)
contradiction. Corollary (Riemann mapping theorem). Any connected and simply connected open domain in the complex plane with at least two boundary points
Planar_Riemann_surface
Process of understanding a complex topic or substance
Analysis (pl.: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The
Analysis
Logarithm of a complex number
holomorphic (that is, complex differentiable) with nonvanishing derivative, the complex analogue of the inverse function theorem applies. It shows that
Complex_logarithm
(mathematical analysis) — bound on maximum of derivative of polynomial in unit disk Mergelyan's theorem — generalization of Stone–Weierstrass theorem for polynomials
List of numerical analysis topics
List_of_numerical_analysis_topics
Measure of algorithmic complexity
determine the probability, divide by 2n. By the above theorem (§ Compression), most strings are complex in the sense that they cannot be described in any
Kolmogorov_complexity
Branch of mathematics
investigated including the proof of the Atiyah–Singer index theorem. The development of complex geometry was spurred on by parallel results in algebraic
Differential_geometry
Commutative algebra theorem
(2011). Stein Manifolds and Holomorphic Mappings: The Homotopy Principle in Complex Analysis. Springer. Theorem 5.3.1, p. 190. ISBN 978-3-642-22250-4.
Quillen–Suslin_theorem
Complex numbers with non-negative imaginary part
axis and thus complex numbers for which y > 0 {\displaystyle y>0} . It is the domain of many functions of interest in complex analysis, especially modular
Upper_half-plane
Locally convex topological vector space that is also a complete metric space
important results in functional analysis, like the open mapping theorem, the closed graph theorem, and the Banach–Steinhaus theorem, still hold. Recall that
Fréchet_space
Mathematical transform that expresses a function of time as a function of frequency
operators Fourier inversion theorem – Mathematical theorem about functions Fourier multiplier – Type of operator in Fourier analysisPages displaying short descriptions
Fourier_transform
Normed vector space that is complete
for example) and guarantees that the Banach–Steinhaus theorem holds. The open mapping theorem implies that when τ 1 {\displaystyle \tau _{1}} and τ 2
Banach_space
Second-order partial differential equation
{\displaystyle u} is harmonic in D {\displaystyle D} , then the divergence theorem implies the compatibility condition ∫ ∂ D ∂ u ∂ ν d S = 0. {\displaystyle
Laplace's_equation
Partial differential equation
simplest applications is to the Riemann mapping theorem for simply connected bounded open domains in the complex plane. When the domain has smooth boundary
Beltrami_equation
All numbers between two given numbers
mathematical analysis. For example, they occur implicitly in the epsilon-delta definition of continuity; the intermediate value theorem asserts that the
Interval_(mathematics)
OPEN MAPPING-THEOREM-COMPLEX-ANALYSIS
OPEN MAPPING-THEOREM-COMPLEX-ANALYSIS
Boy/Male
Welsh
Son of Owen.
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
Male
English
 Anglicized form of Irish Gaelic Eóghan, OWEN means "born of yew." Compare with another form of Owen.
Male
Swedish
Norwegian and Swedish form of Old Norse Óðinn, ODEN means "poetry, song" and "eager, frenzied, raging."
Surname or Lastname
English
English : from Old English Tæpping, an unattested patronymic from Tæppa. Compare Tapp.Joseph Tapping (d. 1678) is buried in King’s Chapel Burying Ground, Boston, MA.
Surname or Lastname
English and Irish
English and Irish : probably a hypercorrected form of Lappin.
Female
English
English short form of Latin Penelope, PEN means "weaver of cunning."
Surname or Lastname
English
English : from a medieval personal name, originally an Old English patronymic from a personal name or byname Tippa, for which there is evidence in place names such as Tiptree, but which is of uncertain origin.
Girl/Female
Greek
Watcher.
Boy/Male
Celtic Welsh
Son of Owen.
Male
Welsh
Variant form of Welsh Owen, possibly OUEN means "born of yew."
Surname or Lastname
English
English : habitational name, probably from Comley in Shropshire or Combley on the Isle of Wight; both are named with Old English cumb ‘valley’ + lēah ‘woodland clearing’.
Female
Thai/Siamese
Thai name PEN-CHAN means "full moon."
Surname or Lastname
English
English : variant of Penn.Dutch : metonymic occupational name for a clerk or penman, from Dutch pen ‘pen’.Cambodian : unexplained.
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from any of various places called Copley, for example in County Durham, Staffordshire, and Yorkshire, from the Old English personal name Coppa (apparently a byname for a tall man) or from copp ‘hilltop’ + lēah ‘woodland clearing’.
Surname or Lastname
English (Devon)
English (Devon) : variant spelling of Appling.
Surname or Lastname
English
English : patronymic from Mann 1 and 2.Irish : adopted as an English equivalent of Gaelic Ó MainnÃn ‘descendant of MainnÃn’, probably an assimilated form of MainchÃn, a diminutive of manach ‘monk’. This is the name of a chieftain family in Connacht. It is sometimes pronounced Ó MaingÃn and Anglicized as Mangan.Anstice Manning, widow of Richard Manning of Dartmouth, England, came to MA with her children in 1679. Her great-great-grandson Robert, born at Salem, MA, in 1784, was the uncle and protector of author Nathaniel Hawthorne. Another early bearer of the relatively common British name was Jeffrey Manning, one of the earliest settlers in Piscataway township, Middlesex Co., NJ. His great-grandson James Manning (1738–91) was a founder and the first president of Rhode Island College (Brown University).
Male
Welsh
 Modern Welsh form of Old Welsh Owain, OWEN means "born of yew." Compare with another form of Owen.
Girl/Female
Egyptian
Great.
Surname or Lastname
English (common in Lancashire and northern Ireland)
English (common in Lancashire and northern Ireland) : from a patronymic or pet form of Topp, or possibly from an unattested Old English personal name Topping.
OPEN MAPPING-THEOREM-COMPLEX-ANALYSIS
OPEN MAPPING-THEOREM-COMPLEX-ANALYSIS
Boy/Male
Indian, Sanskrit
Power
Boy/Male
Hindu
A lamp, Beautiful
Boy/Male
Indian
Holy war
Boy/Male
Greek American Spanish
Defender; protector of mankind. Famous Bearer: Alexander the Great.
Boy/Male
American, British, English
Spear-man
Boy/Male
Tamil
Lord Brahma
Boy/Male
African
Ghanian name given to a child born on Tuesday.
Surname or Lastname
English
English : regional name denoting someone from the county of Berkshire in central southern England. The place name is derived from a Celtic name meaning ‘hilly place’ + Old English scīr ‘shire’.
Girl/Female
American, Australian, Chinese, Greek
Honey Bee
Girl/Female
Indian
Goddess Durga
OPEN MAPPING-THEOREM-COMPLEX-ANALYSIS
OPEN MAPPING-THEOREM-COMPLEX-ANALYSIS
OPEN MAPPING-THEOREM-COMPLEX-ANALYSIS
OPEN MAPPING-THEOREM-COMPLEX-ANALYSIS
OPEN MAPPING-THEOREM-COMPLEX-ANALYSIS
a.
Free; disengaged; unappropriated; as, to keep a day open for any purpose; to be open for an engagement.
a.
Intricate; entangled; complicated; complex.
a.
Complex, complicated.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
a.
Repeatedly compound; made up of complex constituents.
v. t.
To make or set open; to render free of access; to unclose; to unbar; to unlock; to remove any fastening or covering from; as, to open a door; to open a box; to open a room; to open a letter.
v. t.
To enter upon; to begin; as, to open a discussion; to open fire upon an enemy; to open trade, or correspondence; to open a case in court, or a meeting.
adv.
In a complex manner; not simply.
a.
Having the mouth open; gaping; hence, greedy; clamorous.
a.
Not settled or adjusted; not decided or determined; not closed or withdrawn from consideration; as, an open account; an open question; to keep an offer or opportunity open.
a.
Not concealed or secret; not hidden or disguised; exposed to view or to knowledge; revealed; apparent; as, open schemes or plans; open shame or guilt.
a.
Open.
a.
Free or cleared of obstruction to progress or to view; accessible; as, an open tract; the open sea.
v. t.
To spread; to expand; as, to open the hand.
v. t.
To formulate into a theorem.
a.
Of or pertaining to a theorem or theorems; comprised in a theorem; consisting of theorems.
a.
Not drawn together, closed, or contracted; extended; expanded; as, an open hand; open arms; an open flower; an open prospect.
a.
Not complex; uncompounded; simple.
a.
Produced by an open string; as, an open tone.
n.
Open or unobstructed space; clear land, without trees or obstructions; open ocean; open water.