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United States foundational philosophy
constitutional theory, compact theory is an interpretation of the Constitution which asserts the United States was formed through a compact agreed upon by
Compact_theory
Type of continuous linear operator
Compact operators first arose in the theory of integral equations, where many integral operators have compactness properties. They play a central role
Compact_operator
Topological group with compact topology
in significant fashion. Compact groups have a well-understood theory, in relation to group actions and representation theory. In the following we will
Compact_group
Theory in functional analysis
properties of compact operators. The reader will see that most statements transfer verbatim from the matrix case. The spectral theory of compact operators
Spectral theory of compact operators
Spectral_theory_of_compact_operators
1798/99 resolutions against the Alien and Sedition Acts
force whatsoever. The Virginia Resolution of 1798 also relied on the compact theory and asserted that the states have the right to determine whether actions
Kentucky and Virginia Resolutions
Kentucky_and_Virginia_Resolutions
Legal theory in U.S. constitutional law
nullification has. The theory of nullification is based on a view that the states formed the Union by an agreement (or "compact") among the states, and
Nullification (U.S. Constitution)
Nullification_(U.S._Constitution)
Political powers reserved for U.S. states
Kentucky and Virginia Resolutions of 1798-99 first formally stated the compact theory of Union, arguing that the federal government is a creature of the states
States'_rights
1861 speech by Abraham Lincoln
Inaugural can be seen most directly by comparing their arguments for why compact theory does not justify secession, and the language in their penultimate paragraphs:
Abraham Lincoln's first inaugural address
Abraham_Lincoln's_first_inaugural_address
Essay by Jefferson Davis
he had written what is probably the most thorough exegesis of the compact theory of the United States Constitution in existence, devoting the first fifteen
A Short History of the Confederate States of America
A_Short_History_of_the_Confederate_States_of_America
Digital optical disc data storage format
The compact disc (CD) is a digital optical disc data storage format co-developed by Philips and Sony to store and play digital audio recordings. It employs
Compact_disc
Theorem in mathematical logic
countable compactness theorem in 1930. Anatoly Maltsev proved the uncountable case in 1936. The compactness theorem has many applications in model theory; a
Compactness_theorem
Branch of mathematics that studies abstract algebraic structures
developed first by considering the compact groups, to which results of compact representation theory apply. This theory can be extended to finite-dimensional
Representation_theory
Quantum field theory
class of similar theories. The Yang–Mills theory is a gauge theory based on a special unitary group SU(n), or more generally any compact Lie group. A Yang–Mills
Yang–Mills_theory
Type of topology
mathematics, the compact-open topology is a topology defined on the set of continuous maps between two topological spaces. The compact-open topology is
Compact-open_topology
In the mathematical area of order theory, the compact elements or finite elements of a partially ordered set are those elements that cannot be subsumed
Compact_element
Claimed right of a U.S. state
The theory of interposition is grounded in the compact theory of the Constitution, which holds that the states are parties to the federal compact. Its
Interposition
Type of topological group in mathematics
locally compact setting, such techniques need not hold. The resulting theory is a central part of harmonic analysis. The representation theory for locally
Locally_compact_group
Classification in astronomy
In astronomy, the term compact object (or compact star) refers collectively to white dwarfs, neutron stars, and black holes. It could also include exotic
Compact_object
Mathematical manifold theory
smooth or compact. Potential theory Serre duality Helmholtz decomposition Local invariant cycle theorem Arakelov theory Hodge–Arakelov theory ddbar lemma
Hodge_theory
On when a family of real, continuous functions has a uniformly convergent subsequence
with domain a compact metric space (Dunford & Schwartz 1958, p. 382). Modern formulations of the theorem allow for the domain to be compact Hausdorff and
Arzelà–Ascoli_theorem
Type of large cardinal in set theory
axioms of set theory. (Tarski originally called them "not strongly incompact" cardinals.) Formally, a cardinal κ is defined to be weakly compact if it is uncountable
Weakly_compact_cardinal
Concept in political philosophy
In moral and political philosophy, the social contract is an idea, theory, or model that usually, although not always, concerns the legitimacy of the authority
Social_contract
American mathematician (1943–2024)
In 1995, Hamilton extended Jeff Cheeger's compactness theory for Riemannian manifolds to give a compactness theorem for sequences of Ricci flows.[H95a]
Richard_S._Hamilton
Branch of mathematics that studies dynamical systems
area of study are typical of rigidity theory. In the 1930s G. A. Hedlund proved that the horocycle flow on a compact hyperbolic surface is minimal and ergodic
Ergodic_theory
Type of mathematical space
mathematics, especially general topology and mathematical analysis, compactness is a property of a space that makes it behave in many ways like a finite
Compact_space
Introductory statement of the US Constitution's fundamental purposes
the 'compact theory' [of the Constitution] does not justify interposition. Thus, Edward Livingston, ... though an adherent of th[e 'compact] theory['],
Preamble to the United States Constitution
Preamble_to_the_United_States_Constitution
Area of mathematical analysis
analysis, where the emphasis is on symmetry, locally compact groups, and representation theory. A real-variable method in harmonic analysis is to decompose
Harmonic_analysis
Inputs for which a function's value is non-zero
distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In a locally compact Hausdorff
Support_(mathematics)
Mathematical models of strategic interactions
mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by Theory of Games and
Game_theory
Duality for locally compact abelian groups
named after Lev Pontryagin, who laid down the foundations for the theory of locally compact abelian groups and their duality during his early mathematical
Pontryagin_duality
Class of models in the behavioral sciences
use of decision theory (the theory of rational choice) as a set of guidelines to help understand economic and social behavior. The theory tries to approximate
Rational_choice_model
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
tractable representation theory because of the Peter–Weyl theorem. Just like simple complex Lie algebras, centerless compact Lie groups are classified
Simple_Lie_group
Technique in theoretical physics
size of the compact dimension goes to zero, no fields depend on this extra dimension, and the theory is dimensionally reduced. In string theory, compactification
Compactification_(physics)
Nonempty compact connected metric space
"continua") is a nonempty compact connected metric space, or, less frequently, a compact connected Hausdorff space. Continuum theory is the branch of topology
Continuum_(topology)
Objects that generalize functions
theory of hyperfunctions; this theory has a different character from the previous ones because there are no analytic functions with non-empty compact
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
Transfer of certain powers from the United States federal government back to the states
Opportunity Act PL 104-193 Anti-Federalism Classical republicanism Compact theory Convention to propose amendments to the United States Constitution Cooperative
New_Federalism
Left-invariant (or right-invariant) measure on locally compact topological group
the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on
Haar_measure
Mathematics of real numbers and real functions
studies limits, continuity, compactness, differentiation, integration, and series. More advanced courses often include measure theory, Lebesgue integration
Real_analysis
1791 amendment enumerating states' rights
stems from the so-called compact theory suggesting that because the states created the federal government by agreement ("compact") to join the Union, they
Tenth Amendment to the United States Constitution
Tenth_Amendment_to_the_United_States_Constitution
Theory of gravitation as curved spacetime
relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert
General_relativity
Mathematical concept
is the theory of groups. Then Mod(T) is the category of groups, and the compact objects in Mod(T) are the finitely presented groups. The compact objects
Compact_object_(mathematics)
Mathematical theory
Lie theory, there are two definitions of a compact Lie algebra. Extrinsically and topologically, a compact Lie algebra is the Lie algebra of a compact Lie
Compact_Lie_algebra
Type of mathematical measure
have a well defined support. Another approach to measure theory is to restrict to locally compact Hausdorff spaces, and only consider the measures that correspond
Radon_measure
Homology theory for locally compact spaces
support is a homology theory for locally compact spaces, introduced by Armand Borel and John Moore in 1960. For reasonable compact spaces, Borel−Moore homology
Borel–Moore_homology
Subset of a topological space whose closure is compact
compact. Every subset of a compact topological space is relatively compact (since a closed subset of a compact space is compact). In an arbitrary topological
Relatively_compact_subspace
American politician (1791–1839)
Hamilton Jr., a vocal proponent of the doctrines of states' rights, compact theory, and nullification; his 1830 debate in the Senate with Daniel Webster
Robert_Y._Hayne
Riemannian manifold with SU(n) holonomy
(1985), after Eugenio Calabi (1954, 1957), who first conjectured that compact complex manifolds of Kähler type with vanishing first Chern class always
Calabi–Yau_manifold
Russian-French mathematician
Wysocki, K.; Zehnder, E. Compactness results in symplectic field theory. Geom. Topol. 7 (2003), 799–888. Floer, Andreas. Morse theory for Lagrangian intersections
Mikhael Gromov (mathematician)
Mikhael_Gromov_(mathematician)
Theorem in measure theory
In measure theory Prokhorov's theorem relates tightness of measures to relative compactness (and hence weak convergence) in the space of probability measures
Prokhorov's_theorem
Compact astronomical body
an astronomical body so compact that its gravity prevents anything, including light, from escaping. Albert Einstein's theory of general relativity, which
Black_hole
fact in the structure theory of complex semisimple Lie algebras that every such algebra has two special real forms: one is the compact real form and corresponds
Real_form_(Lie_theory)
Duality between a group and its representations
In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. It is
Tannaka–Krein_duality
American political party
state's membership in the Union is voluntary, a stance known as the compact theory. The Constitution Party's 2012 platform called for phasing out social
Constitution Party (United States)
Constitution_Party_(United_States)
French mathematician (born 1956)
all of Euclidean space, where standard compactness theory does not apply, Lions established a number of compactness results for functions with symmetry.[L82b]
Pierre-Louis_Lions
Area of mathematical logic
theory (such as compactness for infinitary logics) have been shown to be equivalent to large cardinal axioms. Abstract model theory Algebraic theory Compactness
Model_theory
Group homomorphism into the general linear group over a vector space
representation theory; this special case has very different properties. See Representation theory of finite groups. Compact groups or locally compact groups —
Group_representation
US interstate water allocation agreement
Colorado River Compact is a 1922 agreement that regulates water distribution among seven states in the Southwestern United States. The compact is about the
Colorado_River_Compact
In set theory, a strongly compact cardinal is a certain kind of large cardinal. An uncountable cardinal κ is strongly compact if and only if every κ-complete
Strongly_compact_cardinal
Topological spaces whose union is a boundary
mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary
Cobordism
Homology Theory in Algebraic Topology is Compactly Supported
In mathematics, a homology theory in algebraic topology is compactly supported if, in every degree n, the relative homology group Hn(X, A) of every pair
Compactly_supported_homology
Indian theoretical physicist
field theory, string theory, supersymmetry, supergravity and superstring theory, Dirac's instant-form and light-front quantization of field theories and
Daya_Shankar_Kulshreshtha
Powers granted by the Constitution to the U.S. federal legislature
the Constitutional authority upon which all legislation is based." Compact theory Constitution in exile New federalism Originalism States' rights Strict
Enumerated_powers
American philosopher
philosophy at Emory University in Atlanta, Georgia. He supports the compact theory of the United States, with its concomitant provisions for corporate
Donald_Livingston
Functional analysis concept
induced by the operator norm. As such, results from matrix theory can sometimes be extended to compact operators using similar arguments. By contrast, the study
Compact operator on Hilbert space
Compact_operator_on_Hilbert_space
Topological group structure arising in Fourier analysis
mathematical areas, including harmonic analysis, topology, and number theory, locally compact abelian groups are abelian groups which have a particularly convenient
Locally_compact_abelian_group
Statement about linear functionals and measures
functionals on spaces of continuous functions on a locally compact space to measures in measure theory. The theorem is named for Frigyes Riesz (1909) who introduced
Riesz–Markov–Kakutani representation theorem
Riesz–Markov–Kakutani_representation_theorem
compact Lie group can be studied through finite-dimensional representations of the universal cover of such a group. Hence, the representation theory of
Representation theory of semisimple Lie algebras
Representation_theory_of_semisimple_Lie_algebras
Branch of mathematics that studies the properties of groups
about Γ. A comparatively recent trend in the theory of finite groups exploits their connections with compact topological groups (profinite groups): for
Group_theory
Small galaxy composed of up to several billion stars
type dwarfs Blue compact dwarf galaxies (see section below) Ultra-compact dwarf galaxies (see section below) In astronomy, a blue compact dwarf galaxy (BCD
Dwarf_galaxy
On when a set of compact Riemannian manifolds of a given dimension is relatively compact
fundamental compactness theorem for sequences of metric spaces. In the special case of Riemannian manifolds, the key assumption of his compactness theorem
Gromov's compactness theorem (geometry)
Gromov's_compactness_theorem_(geometry)
US 1800 government report
been broken by the usurpation of power. This doctrine is known as the compact theory. It was the presence of this argument in the Resolutions that had allowed
Report_of_1800
Democratic provision limiting majority rule
"Tariff of Abominations." Nullification, an outgrowth of Jeffersonian compact theory, held that any state, as part of its rights as sovereign parties to
Concurrent_majority
Type of mathematical convergence in topology
In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence that generalizes the idea of uniform convergence.
Compact_convergence
Event during the presidency of Andrew Jackson
Quincy Adams, Nathaniel Chipman, and Nathan Dane. They rejected the compact theory advanced by Calhoun, claiming that the Constitution was the product
Nullification_crisis
Branch of differential geometry
are about. Gauss–Bonnet theorem The integral of the Gauss curvature on a compact 2-dimensional Riemannian manifold is equal to 2πχ(M) where χ(M) denotes
Riemannian_geometry
Data format used for audio compact discs
Compact Disc Digital Audio (CDDA or CD-DA), also known as Digital Audio Compact Disc or simply as Audio CD, is the standard format for audio compact discs
Compact_Disc_Digital_Audio
Technique in mathematics
groups Holomorphic functional calculus Spectral theory Compact operator Laplace transform Fredholm theory Liouville–Neumann series Decomposition of spectrum
Resolvent_formalism
Conspiracy theory about race and culture
theory or great replacement theory, is a debunked white nationalist far-right conspiracy theory coined by French author Renaud Camus. Camus's theory states
Great Replacement conspiracy theory
Great_Replacement_conspiracy_theory
Scientific study of digital information
invention of the compact disc, the feasibility of mobile phones and the development of the Internet and artificial intelligence. The theory has also found
Information_theory
cohomology with compact support refers to certain cohomology theories, usually with some condition requiring that cocycles should have compact support. Let
Cohomology with compact support
Cohomology_with_compact_support
Group that is also a differentiable manifold with group operations that are smooth
semisimple Lie algebras, Cartan's theory of symmetric spaces, and Hermann Weyl's description of representations of compact and semisimple Lie groups using
Lie_group
Property of a mathematical space
completion, of the kind that string theory is intended to provide. In particular, superstring theory requires six compact dimensions (6D hyperspace) forming
Dimension
Concept in topology
In mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst
Maximal_compact_subgroup
Branch of mathematics that studies sets
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any
Set_theory
Pseudonym of an Anti-Federalist opposed to the ratification of the Constitution
advisory. The letters indicate that the Federal Farmer ascribed to the compact theory of federalism. The threat to federal government constituted a menace
Federal_Farmer
American mathematician (1933–2026)
inquiry of rotating fluids. The result of which, was a complete and compact theory, supported by simple yet profound experiments. These experiments demonstrated
Harvey_P._Greenspan
Embedding a topological space into a compact space as a dense subset
is the process or result of making a topological space into a compact space. A compact space is a space in which every open cover of the space contains
Compactification (mathematics)
Compactification_(mathematics)
Study of Lie groups, Lie algebras and differential equations
spacetime. The one-parameter groups are the first instance of Lie theory. The compact case arises through Euler's formula in the complex plane. Other one-parameter
Lie_theory
Basic result in harmonic analysis on compact topological groups
Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not necessarily abelian. It
Peter–Weyl_theorem
Concept in mathematics
unitary operator for every g ∈ G. The general theory is well-developed in the case that G is a locally compact (Hausdorff) topological group and the representations
Unitary_representation
Theory of subatomic structure
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called
String_theory
Compactness theorem in Yang–Mills theory
In differential geometry and in particular Yang–Mills theory, Uhlenbeck's compactness theorem is a result about sequences of (weak Yang–Mills) connections
Uhlenbeck's compactness theorem
Uhlenbeck's_compactness_theorem
In algebra, a locally compact field is a topological field whose topology forms a locally compact Hausdorff space. These kinds of fields were originally
Locally_compact_field
locally compact?". Mathematics Stack Exchange. "A $\sigma$-compact but not hemicompact space?". Mathematics Stack Exchange. Leon Ehrenpreis, Theory of Distributions
Exhaustion_by_compact_sets
(pseudo-)Riemannian manifold whose geodesics are reversible
H is compact. Riemannian symmetric spaces arise in a wide variety of situations in both mathematics and physics. Their central role in the theory of holonomy
Symmetric_space
Dutch engineer, inventor, and entrepreneur (born 1946)
and the Compact Disc". IEEE Information Theory Society Newsletter. 57: 42–46. Retrieved 5 February 2018. K. Schouhamer Immink (1998). "Compact Disc Story"
Kees_Schouhamer_Immink
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
Representation theory of an important group in physics
the representation theory of the Poincaré group is an example of the representation theory of a Lie group that is neither a compact group nor a semisimple
Representation theory of the Poincaré group
Representation_theory_of_the_Poincaré_group
Algebraic structure used in topology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a way of attaching algebraic invariants to a topological space or
Cohomology
Concept in topology
unique "most general" compact Hausdorff space generated by X, in the sense that any continuous map from X into any other compact Hausdorff space factors
Stone–Čech_compactification
COMPACT THEORY
COMPACT THEORY
Boy/Male
Indian, Tamil
No Compare
Girl/Female
Arabic
Sensible Contact
Boy/Male
Indian, Sanskrit
Fallen from Glory
Girl/Female
Muslim
Beauty of company
Boy/Male
Indian, Punjabi, Sikh
Lord's Company
Girl/Female
Arabic, Muslim
Beauty of Company
Girl/Female
Hindu, Indian, Marathi, Tamil
Compact; Promise
Boy/Male
Indian, Punjabi, Sikh
Liberation through Company
Surname or Lastname
Americanized form of German Eisele. Compare Isley.English
Americanized form of German Eisele. Compare Isley.English : unexplained. This name is quite widespread in Britain.
Boy/Male
Indian, Punjabi, Sikh
Good Company
Girl/Female
Hindu, Indian
Compare
Girl/Female
Indian, Telugu
Good Company
Boy/Male
Hindu, Indian, Sanskrit
Company
Girl/Female
Tamil
Compare
Boy/Male
Hindu, Indian
Compact; Safe; Secure
Boy/Male
Indian, Punjabi, Sikh
Company of Guru
Girl/Female
Arabic, Muslim
Beauty of Company
Boy/Male
Hindu, Indian
Compact; Firm; Solid
Boy/Male
Hindu, Indian, Sanskrit
In the Company
Surname or Lastname
Americanized spelling of German Kahle. Compare Kahley or Köhler (see Kohler).English and Manx
Americanized spelling of German Kahle. Compare Kahley or Köhler (see Kohler).English and Manx : variant spelling of Caley.
COMPACT THEORY
COMPACT THEORY
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
By the Safe; Happy; Expert; Well Being
Girl/Female
Arabic, Muslim
Princess
Boy/Male
Tamil
Crown given by Indra to Arjuna, Another name of Arjun
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu, Traditional
Goddess of Knowledge; Goddess Parvati / Saraswati
Girl/Female
Tamil
Goddess of Matanga, Goddess Durga
Surname or Lastname
English
English : from Middle English colhope, col(l)hop ‘fried eggs and ham or bacon’, which Reaney believes to have been applied as a metonymic occupational name for the keeper of a cook house.
Girl/Female
Arabic, Australian, Muslim
Favoured by God; Consent
Girl/Female
English
Famous.
Girl/Female
Indian, Sanskrit
Moonlight; Moon's Rays
Surname or Lastname
English
English : unexplained.
COMPACT THEORY
COMPACT THEORY
COMPACT THEORY
COMPACT THEORY
COMPACT THEORY
v. t.
To manure with compost.
n.
One who makes a compact.
a.
Strong; firm; compact.
v. t.
To compact or join anew.
imp. & p. p.
of Compact
n.
An inclosing limit; boundary; circumference; as, within the compass of an encircling wall.
n.
The crew of a ship, including the officers; as, a whole ship's company.
n.
Extent; reach; sweep; capacity; sphere; as, the compass of his eye; the compass of imagination.
n.
A mixture for fertilizing land; esp., a composition of various substances (as muck, mold, lime, and stable manure) thoroughly mingled and decomposed, as in a compost heap.
p. p. & a
Brief; close; pithy; not diffuse; not verbose; as, a compact discourse.
p. pr. & vb. n.
of Compact
n.
Guests or visitors, in distinction from the members of a family; as, to invite company to dine.
v. i.
To be like or equal; to admit, or be worthy of, comparison; as, his later work does not compare with his earlier.
n.
Contact or impression by touch; collision; forcible contact; force communicated.
v. i.
To bear or endure; to put up (with); as, to comport with an injury.
n.
An association of persons for the purpose of carrying on some enterprise or business; a corporation; a firm; as, the East India Company; an insurance company; a joint-stock company.
adv.
In a compact manner; with close union of parts; densely; tersely.
v. t.
To mingle, as different fertilizing substances, in a mass where they will decompose and form into a compost.
a.
Compact; pressed close; concentrated; firmly united.