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Topics referred to by the same term
mathematics, compactly generated can refer to: Compactly generated group, a topological group which is algebraically generated by one of its compact subsets
Compactly_generated
Property of topological spaces
space X {\displaystyle X} is called a compactly generated space or k-space if its topology is determined by compact spaces in a manner made precise below
Compactly_generated_space
mathematics, a compactly generated (topological) group is a topological group G which is algebraically generated by one of its compact subsets. This should
Compactly_generated_group
Category in mathematics
explain the name: if a localizing subcategory S of a compactly generated triangulated category D is generated by a set of objects, then there is a Bousfield
Triangulated_category
Mathematical concept
D({\text{Sh}}(X;{\text{Ab}}))} for a non-compact topological space X {\displaystyle X} , it is generally not a compactly generated category. Some evidence for this
Compact_object_(mathematics)
Type of topology
coincides with the compact-open topology and may be used to uniquely define it. The modification of the definition for compactly generated spaces may be viewed
Compact-open_topology
Category used in algebraic topology
In mathematics, the category of compactly generated weak Hausdorff spaces, CGWH, is a category used in algebraic topology as an alternative to the category
Category of compactly generated weak Hausdorff spaces
Category_of_compactly_generated_weak_Hausdorff_spaces
Type of topological space
that X and Y are compactly generated Hausdorff spaces, so Hom(X,Y) is often taken with the compactly generated variant of the compact-open topology; the
CW_complex
Category whose objects are topological spaces and whose morphisms are continuous maps
topological manifolds, with compactly generated spaces as objects and continuous maps as morphisms or with the category of compactly generated weak Hausdorff spaces
Category of topological spaces
Category_of_topological_spaces
Continuous deformation between two continuous functions
homotopies with certain spaces. Algebraic topologists work with compactly generated spaces, CW complexes, or spectra. Formally, a homotopy between two
Homotopy
often used in tandem with compactly generated spaces in algebraic topology. For that, see the category of compactly generated weak Hausdorff spaces. Their
Weak_Hausdorff_space
Type of topological space in mathematics
locally compact Hausdorff spaces are compactly generated. Conversely, every compactly generated Hausdorff space is a quotient of some locally compact Hausdorff
Locally_compact_space
Type of mathematical space
compact. Compactly generated space Compactness theorem Continuous functions on a compact Hausdorff space Eberlein compactum Exhaustion by compact sets Lindelöf
Compact_space
Type of mathematical convergence in topology
converges compactly to some continuous map. If f n → f {\displaystyle f_{n}\to f} uniformly, then f n → f {\displaystyle f_{n}\to f} compactly. If ( X
Compact_convergence
Mathematical construction used in homotopy theory
a geometric realization functor which turns simplicial sets into compactly generated Hausdorff spaces. Most classical results on CW complexes in homotopy
Simplicial_set
Hypothetical object usable as a time machine
singularities" and proves that "[t]here will be a Cauchy horizon that is compactly generated and that in general contains one or more closed null geodesics which
Tipler_cylinder
Topological space characterized by sequences
is compactly generated, and finite products in Seq coincide with those for compactly generated spaces, since products in the category of compactly generated
Sequential_space
On when a family of real, continuous functions has a uniformly convergent subsequence
for a family of functions from a compactly generated Hausdorff space into a uniform space to be compact in the compact-open topology; see Kelley (1991
Arzelà–Ascoli_theorem
Topics referred to by the same term
particle k-space (magnetic resonance imaging) Another name for a compactly generated space in topology K-space (functional analysis) is an F-space such
K-space
Categorical treatment of topological spaces
topological category is a category that is enriched over the category of compactly generated Hausdorff spaces. They can be used as a foundation for higher category
Topological category (enriched category theory)
Topological_category_(enriched_category_theory)
Topology determined by family of subspaces
subspaces. Compactly generated spaces (in the sense of Definition 1 in that article) are those determined by the family of all their compact subspaces
Coherent_topology
Transforming a function in such a way that it only takes a single argument
{\displaystyle X} , Y {\displaystyle Y} and Y X {\displaystyle Y^{X}} are compactly generated, although there are more cases. One useful corollary is that a function
Currying
Hypothetical travel into the past or future
build a time machine of a special type (a "time machine with the compactly generated Cauchy horizon") in a region where the weak energy condition is satisfied
Time_travel
Mathematics glossary
this can be taken to mean for example, a space is a CW complex or compactly generated weakly Hausdorff space. Similarly, no attempt is made to be definitive
Glossary of algebraic topology
Glossary_of_algebraic_topology
finite algebra. A lattice is called algebraic if it is complete and compactly generated. In 1963, Grätzer and Schmidt proved that every algebraic lattice
Finite lattice representation problem
Finite_lattice_representation_problem
Mathematical map between topological spaces
{\displaystyle Y} is a compactly generated Hausdorff space (this includes Hausdorff spaces that are either first-countable or locally compact), then f {\displaystyle
Proper_map
On representability of a contravariant functor on the category of connected CW complexes
adjoint functor. Namely, if C and D are triangulated categories with C compactly generated and F a triangulated functor commuting with arbitrary direct sums
Brown's representability theorem
Brown's_representability_theorem
Conjecture that the laws of physics prevent closed timelike curves
Wald, Robert (1997). "Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon". Communications in Mathematical Physics. 183 (3):
Chronology protection conjecture
Chronology_protection_conjecture
Continuous closed surjective map, each of whose fibers are also compact sets
proper maps are perfect, provided the topology of Y is Hausdorff and compactly generated. Open and closed maps – Functions that send open (resp. closed) subsets
Perfect_map
Relation among continuous functions
Uniform restraint of the change in functions More generally, on any compactly generated space; e.g., a first-countable space. Rudin 1991, p. 44 §2.5. Reed
Equicontinuity
Lattice whose elements are the subgroups of a given group
subgroups are algebraic lattices. This means that they are complete and compactly generated. However in general, there is no restriction on the possible sublattices
Lattice_of_subgroups
Continuous, position-preserving mapping from a topological space into a subspace
injective, in fact a homeomorphism to its image. If X is Hausdorff (or a compactly generated weak Hausdorff space), then the image of a cofibration f is closed
Retraction_(topology)
the Banach space ℓ 1 {\displaystyle \ell ^{1}} is not a K-space. Compactly generated space – Property of topological spaces Gelfand–Shilov space Kalton
K-space_(functional_analysis)
Generalization of category theory
convenient category of topological spaces, e.g. the category of compactly generated Hausdorff spaces. These are models of higher categories introduced
Higher_category_theory
a Brauner space is a complete compactly generated locally convex space X {\displaystyle X} having a sequence of compact sets K n {\displaystyle K_{n}}
Brauner_space
Branch of mathematics
instead, one requires spaces to meet extra constraints, such as being compactly generated weak Hausdorff or a CW complex. In the same vein as above, a "map"
Homotopy_theory
a complete compactly generated locally convex topological vector space X {\displaystyle X} having a universal compact set, i.e. a compact set K {\displaystyle
Smith_space
property Compactification Measure of non-compactness Paracompact space Locally compact space Compactly generated space Axiom of countability Sequential
List of general topology topics
List_of_general_topology_topics
Category admitting tensor products
and R as the unit. The category of pointed spaces (restricted to compactly generated spaces for example) is monoidal with the smash product serving as
Monoidal_category
Topological space where each point has a countable neighbourhood basis
{\displaystyle \left[0,\omega _{1}\right).} Every first-countable space is compactly generated. Every subspace of a first-countable space is first-countable. Any
First-countable_space
Type of category in category theory
Substitute categories have therefore been considered: the category of compactly generated Hausdorff spaces is Cartesian closed, as is the category of Frölicher
Cartesian_closed_category
Finest topology making some functions continuous
discussion here. As an example, a commonly used variant of the notion of compactly generated space is defined as the final topology with respect to a proper class
Final_topology
Generalization of a category
{\displaystyle C} be a Top-enriched category (where Top is the category of compactly generated weak Hausdorff spaces). Then the counit map | Map C [ N h c S ( C
Quasi-category
Combination of pointed topological spaces
Y, and Z in an appropriate "convenient" category (e.g., that of compactly generated spaces), there are natural (basepoint preserving) homeomorphisms
Smash_product
Wavelet constructed using a spline function
j}c_{m+n-j-1}.} The spline wavelets generated using the interpolatory wavelets are not compactly supported. Compactly supported B-spline wavelets were discovered
Spline_wavelet
Completion of the usual space with "points at infinity"
spaces and geomodular lattices, namely, subdirectly irreducible, compactly generated, complemented, modular lattices. Dimension 0 (no lines): The space
Projective_space
Digital optical disc data storage format
represented generated 12% each of the French music industry revenues. Sony and Philips received praise for the development of the compact disc from professional
Compact_disc
Categorical generalization of a function space in set theory
spaces is, for example, given by the full subcategory spanned by the compactly generated Hausdorff spaces. In functional programming languages, the morphism
Exponential_object
Topological space with a distinguished point
it is true for some more restricted categories of spaces, such as compactly generated weak Hausdorff ones. The reduced suspension Σ X {\displaystyle \Sigma
Pointed_space
Amenable group Capable group Commensurability (group theory) Compact group Compactly generated group Complete group Complex reflection group Congruence subgroup
List_of_group_theory_topics
Concept in math
lack any topology. Some topologists prefer instead to work with compactly generated weak Hausdorff spaces; again, with the standard model structure,
Homotopy_category
Abstract mathematical spacetime
of causality since it contains both closed timelike curves and a compactly generated Cauchy horizon, while still being flat (since it is just Minkowski
Misner_space
locally compact abelian group G {\displaystyle G} , let A {\displaystyle A} be a compactly generated subgroup, and B {\displaystyle B} a compact subgroup
Schwartz–Bruhat_function
to install a topology on B(G, X), one needs to demand that X be compactly generated and that G be an abelian topological monoid. Define Bn(G, X) to be
Symmetric_product_(topology)
Concept in homotopy theory
{\displaystyle g\colon A\to B} is any (continuous) map (between compactly generated spaces), and i : A → X {\displaystyle i\colon A\to X} is a cofibration
Cofibration
Class of algebraic theorems
locally rigid. A uniform lattice Γ {\displaystyle \Gamma } in any compactly generated topological group G {\displaystyle G} is topologically locally rigid
Local_rigidity
objects of the category of "reasonable" spaces; e.g., the category of compactly generated weak Hausdorff spaces. Davis & Kirk 2001, Theorem 6.15. 2. Davis
Path_space_fibration
Mathematical object
∗ {\displaystyle {\text{Top}}_{*}} denote the category of based, compactly generated, weak Hausdorff spaces, and Spectra ∗ {\displaystyle {\text{Spectra}}_{*}}
Spectrum_(topology)
The compact elements of Sub(A) are exactly the finitely generated substructures of A. Every substructure is the union of its finitely generated substructures;
Compact_element
Compressed-air engine
motor), do not require an auxiliary speed controller (adding to its compactness), generate less heat, and can be used in more volatile atmospheres as they
Pneumatic_motor
weakly compact subset of Y . {\displaystyle Y.} for every weakly compactly generated Banach space Y , {\displaystyle Y,} every bounded linear operator
Grothendieck_space
In mathematics, process for extending a category
not be compact in C. Conversely, any compact object in Ind(C) arises as the image of an object in X. A category C is called compactly generated, if it
Ind-completion
Algebraic structure of set algebra
x_{3},\dots ):x_{i}\in \{H,T\},i\geq 1\}.} The full sigma algebra can be generated from an ascending sequence of subalgebras, by considering the information
Σ-algebra
Mathematician
1016/j.physd.2022.133559 Jintao Wang, Desheng Li, Jinqiao Duan, Compactly generated shape index theory and its application to a retarded nonautonomous
Jinqiao_Duan
is compact. A finitely generated free group is compact. A trace monoid on a finite set of generators is compact. The bicyclic monoid is not compact. The
Compact_semigroup
Group type in algebra
generated. Every quotient of a finitely generated group G is finitely generated; the quotient group is generated by the images of the generators of G under
Finitely_generated_group
Semi-automatic pistol
ejection port cut-out in the slide. When a cartridge is fired, pressures generated by the ignited powder drive the cartridge casing back against the breech
Heckler_&_Koch_USP
Generalized function whose value is zero everywhere except at zero
a compactly supported function, are needed to ensure pointwise convergence almost everywhere. If the initial η = η1 is itself smooth and compactly supported
Dirac_delta_function
widely used, the Baire sets of a locally compact Hausdorff space form the smallest σ-algebra such that all compactly supported continuous functions are measurable
Baire_set
Fluorescent lamps with folded tubes, often with built-in ballast
Compact fluorescent lamp (CFL) examples A compact fluorescent lamp (CFL), also called compact fluorescent light, energy-saving light and compact fluorescent
Compact_fluorescent_lamp
Argentine football player and manager (1960–2020)
realizing it was a nightmare after having too much of the drink. This generated some controversy in the Argentine media after its release (although the
Diego_Maradona
Topological concept in mathematics
closed manifold is a Euclidean neighborhood retract and thus has finitely generated homology groups. If M {\displaystyle M} is a closed connected n-manifold
Closed_manifold
On the finite presentability of fundamental groups of 3-manifolds
(not necessarily compact) with finitely generated fundamental group, there is a compact three-dimensional submanifold, called the compact core or Scott core
Scott_core_theorem
Machine to increase pressure of gas by reducing its volume
built in urban areas. Also known as a trompe. A mixture of air and water generated through turbulence is allowed to fall into a subterranean chamber where
Compressor
Prolog implementation
and Quintus Prolog de-facto standards, very good performance, and compact generated code. Execution profiling and native code compilation were also added
SICStus_Prolog
Type of information retrieval using LLMs
misinterpret the context. MIT Technology Review gives the example of an AI-generated response stating, "The United States has had one Muslim president, Barack
Retrieval-augmented generation
Retrieval-augmented_generation
Tool in algebraic topology
E) is a finitely generated R-module. Then the cohomology groups Hj(X,E) are finitely generated R-modules. For example, for a compact Hausdorff space X
Sheaf_cohomology
US interstate water allocation agreement
irrigate its lands and to obtain a portion of the electrical power revenue generated by future dams. There was also fear that Mexico would usurp the surplus
Colorado_River_Compact
a topology τ on a set X is the topology τ* whose closed sets are generated by compact saturated subsets of (X, τ). R. Kopperman (1995), Asymmetry and duality
De_Groot_dual
Camera that captures photographs or video in digital format
main imager. Some compact digital cameras use a hybrid autofocus system similar to what is commonly available on DSLRs. Typically, compact digital cameras
Digital_camera
Soft, brown, combustible, sedimentary rock
traditional brown-coal-fired plants are generally much higher per megawatt-hour generated than for comparable black-coal plants, with the world's highest-emitting
Lignite
Tiling of hyperbolic 3-space by uniform polyhedra
hyperbolic space there are nine Coxeter group families of compact convex uniform honeycombs, generated as Wythoff constructions, and represented by permutations
Uniform honeycombs in hyperbolic space
Uniform_honeycombs_in_hyperbolic_space
Type of topological space in mathematics
topology, i.e., the topology generated by all intervals ( x , ∞ ) . {\displaystyle (x,\infty ).} The space is limit point compact because given any point a
Limit_point_compact
U.S. interstate compact
Compact (MHEC) is a regional interstate compact that promotes cooperation and resource sharing in higher education. The member states of the Compact are
Midwestern Higher Education Compact
Midwestern_Higher_Education_Compact
American carbon emission trading program
how they invest RGGI auction proceeds. They have reinvested proceeds, generated by RGGI auctions in a wide variety of programs. Programs funded through
Regional Greenhouse Gas Initiative
Regional_Greenhouse_Gas_Initiative
Select-fire self-loading rifle that fires an intermediate-power cartridge
characteristics as the StG 44. The U.S. Army defines assault rifles as "short, compact, selective-fire weapons that fire a cartridge intermediate in power between
Assault_rifle
Theorem in mathematical logic
In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model
Compactness_theorem
Compaction of ceramic powders is a forming technique for ceramics in which granular ceramic materials are made cohesive through mechanical densification
Compaction_of_ceramic_powders
American political commentator and activist (born 1996)
anti-Zionist and "White Jihad" movements. Observers from Vice News and Compact Magazine have argued that MAGA Communism lacks ideological consistency
Haz_Al-Din
Dam in Quebec, Canada
Histoire du Québec contemporain - Volume 2: Le Québec depuis 1930, Boréal Compact (in French), Montreal: Boréal, ISBN 2-89052-298-9 Paradis, Paul (1967)
Daniel-Johnson_dam
Association football tournament in South Africa
7.4 million unique viewers tuned in for matches. In total, ESPN3.com generated 942 million minutes of viewing or more than two hours per unique viewer
2010_FIFA_World_Cup
Football tournament
increase from the month-long event. The governing body of the sport, FIFA, generated $4.8 billion in revenue from the 2014 tournament, and $6.1 billion from
FIFA_World_Cup
Type of semi-automatic pistol
45 ACP) and Compact versions are manufactured in Italy. The Px4 Subcompact is manufactured in the United States. The full size and Compact versions use
Beretta_Px4_Storm
Association football tournament in Qatar
World Cup in Qatar, which was graded as having "high operational risk", generated criticism from media commentators. It was criticised by many as being
2022_FIFA_World_Cup
Topological structure in number theory
is additive for short exact sequences of finitely-generated modules. The rank of a finitely generated module is zero if and only if the module is a torsion
Iwasawa_algebra
Conversion of character sequences into token sequences in computer science
into template code for compiling and executing). Regular expressions compactly represent patterns that the characters in lexemes might follow. For example
Lexical_analysis
Special dagger category that is compact
In category theory, a branch of mathematics, dagger compact categories (or dagger compact closed categories) first appeared in 1989 in the work of Sergio
Dagger_compact_category
2017 film by Johannes Roberts
Johannes Roberts' mostly underwater thriller is a compact and sturdily crafted B-movie that generates enough scares and suspense to qualify as — well,
47_Meters_Down
Mathematical term in group theory
group is a finitely generated group constructed by Rostislav Grigorchuk that provided the first example of a finitely generated group of intermediate
Grigorchuk_group
Direct summand of a free module (mathematics)
the ring). The converse is true for finitely generated modules over Noetherian rings: a finitely generated module over a commutative Noetherian ring is
Projective_module
COMPACTLY GENERATED
COMPACTLY GENERATED
Surname or Lastname
English and Irish
English and Irish : from the Old Norse personal name þorkell, a contracted form of a name composed of the elements þórr, name of the Scandinavian god of thunder (see Thor) + ketill ‘cauldron’. The personal name Thurkill or Thirkill was in use throughout England in the Middle Ages; in northern England it had been introduced directly by Scandinavian settlers, whereas in the South it was the result of Norman influence. This surname and its variants are especially common in East Anglia. In Ireland the Old Norse name was adopted as a Gaelic personal name (Thorcall), which generated the surnames McCorkle and Corkill.
Surname or Lastname
English
English : variant of Allen.German : habitational name from either of two places called Alling, one in Bavaria and one in Austria.Danish : habitational name from any of several places called Alling. The etymology of the place name is uncertain; it may be a derivative of al ‘alder’.Roger Alling signed the New Haven, CT, Compact in 1639.
Boy/Male
Hindu, Indian
Compact; Firm; Solid
Girl/Female
Hindu, Indian, Marathi, Tamil
Compact; Promise
Boy/Male
Hindu, Indian
Self Generated; Lord Shiva
Boy/Male
Indian, Telugu
Generated
Boy/Male
Hindu
Compact, Massive, Widespread, Great, Large, Mighty, Powerful, Bright, Clear, Name of Vishnu
Surname or Lastname
English
English : habitational name from any of the many places, large and small, called Bradford; in particular the city in West Yorkshire, which originally rose to prosperity as a wool town. There are others in Derbyshire, Devon, Dorset, Greater Manchester, Norfolk, Somerset, and elsewhere. They are all named with Old English brÄd ‘broad’ + ford ‘ford’.This name was brought independently to North American by many different bearers from the 17th century onward. William Bradford (1590–1657), born in Austerfield in South Yorkshire, England, the son of a yeoman farmer, was among the Pilgrim Fathers who emigrated to America on the Mayflower in 1620. He was a signer of the Mayflower Compact and in 1621 he was elected governor of Plymouth colony, being re-elected thirty times.
Boy/Male
Tamil
Compact, Massive, Widespread, Great, Large, Mighty, Powerful, Bright, Clear, Name of Vishnu
Boy/Male
Hindu, Indian
Compact; Safe; Secure
COMPACTLY GENERATED
COMPACTLY GENERATED
Boy/Male
Muslim
Surname or Lastname
English
English : from the medieval personal name Hobb(e) (see Hobbs).Dutch : from Middle Dutch hoppe ‘hops’, hence a metonymic occupational name for a grower or seller of hops.Dutch : from a pet form of the personal name Hubrecht (see Hubert).South German : variant of Hoppe 3.North German form of Hopf.
Girl/Female
Indian
Diminutive of Chandana
Boy/Male
Muslim/Islamic
Helper succourer
Female
Hebrew
(×‘Ö¼Ö´×™× Ö¸×”) Hebrew name BINA means "intelligence, wisdom."Â
Biblical
guide or he directs,
Boy/Male
Tamil
Aanandswarup | ஆநஂதஸà¯à®µà®°à¯‚ப
Full of Joy
Girl/Female
Hindu, Indian
Its a Buddhist Hindu Shrine in India
Boy/Male
Arabic, Muslim, Pashtun
Authority of Everyone
Boy/Male
Christian & English(British/American/Australian)
Illustriously Brilliant
COMPACTLY GENERATED
COMPACTLY GENERATED
COMPACTLY GENERATED
COMPACTLY GENERATED
COMPACTLY GENERATED
p. p. & a
Brief; close; pithy; not diffuse; not verbose; as, a compact discourse.
p. p. & a
Composed or made; -- with of.
imp. & p. p.
of Compact
p. pr. & vb. n.
of Compact
adv.
In a compact manner.
a.
Compact; pressed close; concentrated; firmly united.
adv.
In a compact manner; with close union of parts; densely; tersely.
adv.
Neatly.
a.
That may be compacted.
a.
Collected; compact; close.
n.
An agreement between parties; a covenant or contract.
a.
Strong; firm; compact.
adv.
In a solid manner; densely; compactly; firmly; truly.
n.
One who makes a compact.
v. t.
To thrust, drive, or press closely together; to join firmly; to consolidate; to make close; -- as the parts which compose a body.
a.
Condensed; compact; dense.
p. p. & a
Closely or firmly united, as the particles of solid bodies; firm; close; solid; dense.
p. p. & a
Joined or held together; leagued; confederated.
v. t.
To unite or connect firmly, as in a system.
a.
Banded or compacted together.