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members above the compact element. This notion of compactness simultaneously generalizes the notions of finite sets in set theory, compact sets in topology
Compact_element
Topics referred to by the same term
Compact for Migration, a UN non-binding intergovernmental agreement Compact element, those elements of a partially ordered set that cannot be subsumed
Compact
Type of mathematical space
numbers has a greatest element and a least element. Let X be a totally ordered set endowed with the order topology. Then X is compact if and only if X is
Compact_space
Compact crossover SUV by Honda, 2003–2011
The Honda Element (Japanese: ホンダ・エレメント, Hepburn: Honda Eremento) is a compact crossover SUV manufactured by Honda and marketed in North America over a
Honda_Element
Topological group with compact topology
subsection. Any compact Lie group G has an identity component G0, defined as the connected component of the group in which the identity element lies. The quotient
Compact_group
Chemical element with atomic number 80 (Hg)
Mercury is a chemical element; it has symbol Hg and atomic number 80. It is commonly known as quicksilver. A heavy, silvery d-block element, mercury is the
Mercury_(element)
Individual component of an HTML document
An HTML element is a type of HTML (HyperText Markup Language) document component, one of several types of HTML nodes (some common node types include document
HTML_element
Generalization of compactness
related branches of mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. A totally
Totally_bounded_space
when a top element (the infimum of the empty set) is adjoined to a Scott domain, one can conclude that: the new top element is compact (since the order
Scott_domain
{N} } . s ( x ) = 1 {\displaystyle s(x)=1} , whenever x in G is a compact element. s ( x n ) = s ( x ) n {\displaystyle s(x^{n})=s(x)^{n}} for every
Totally_disconnected_group
Type of data structure
architecture, and implementation. Memory-wise, arrays are compact data structures with no per-element overhead. There may be a per-array overhead (e.g., to
Array_(data_structure)
Pure-injective modules in mathematics
one for each element of I; MI denotes the product of copies of M, one for each element of I). Every indecomposable algebraically compact module has a
Algebraically_compact_module
Specific element of an algebraic structure
mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied
Identity_element
Property in general topology
Concept in mathematics Ultrafilter on a set – Maximal proper filter Compact element- Generalization to lattices Joshi 1983, pp. 242−248. Dolecki & Mynard
Finite_intersection_property
(infimum, meet) Limit superior and limit inferior Irreducible element Prime element Compact element Cofinal and coinitial set, sometimes also called dense Meet-dense
List_of_order_theory_topics
atomic measure. A random set is a set-valued random element. One specific example is a random compact set. Let ( M , d ) {\displaystyle (M,d)} be a complete
Random_element
2003 studio album by Element Eighty
music with extreme vocals. All tracks are written by Element Eighty. "Element Eighty Review | Compact Discs | Reviews @ Ultimate-Guitar.Com". www.ultimate-guitar
Element_Eighty_(album)
Any one of the distinct objects that make up a set in set theory
In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. For example, given a set called A containing
Element_of_a_set
Distinguished element of a Lie algebra's center
In mathematics, a Casimir element (also known as a Casimir invariant or Casimir operator) is a distinguished element of the center of the universal enveloping
Casimir_element
Type of continuous linear operator
In functional analysis, a branch of mathematics, a compact operator is a linear operator that behaves, in several important respects, like a finite-dimensional
Compact_operator
Algebraic ring without a multiplicative identity
functions decreasing to zero at infinity, especially those with compact support on some (non-compact) space. Rngs appear in the following chain of class inclusions:
Rng_(algebra)
Type of large cardinal in set theory
2-element subsets of κ, and a subset S of κ is homogeneous for f if either all of [S]2 maps to 0 or all of it maps to 1. The name "weakly compact" refers
Weakly_compact_cardinal
Topics referred to by the same term
preceding 61 one of the years 60 BC, AD 60, 1960, 2060 Neodymium, the 60th element The international calling code for Malaysia <, the ASCII character with
60
Oligarchic political clique in Upper Canada (1810s to 1840s)
The Family Compact was a small closed group of men who exercised most of the political, economic and judicial power in Upper Canada (mostly analogous
Family_Compact
Topological complex vector space
{\displaystyle C_{0}(X)} has a multiplicative unit element if and only if X {\displaystyle X} is compact. As does any C*-algebra, C 0 ( X ) {\displaystyle
C*-algebra
Bounded sequence in finite-dimensional Euclidean space has a convergent subsequence
sequentially compact if every sequence { x n } {\displaystyle \{x_{n}\}} in A {\displaystyle A} has a convergent subsequence converging to an element of A {\displaystyle
Bolzano–Weierstrass_theorem
Concept in topology
meaning that given two maximal compact subgroups K and L, there is an element g ∈ G such that gKg−1 = L. Hence a maximal compact subgroup is essentially unique
Maximal_compact_subgroup
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
trace of an element of a compact Lie group acting in given setting in terms of the integral over the fixed points of the element. If the element is neutral
Equivariant_index_theorem
Theorem in representation theory
related theorem classifying the irreducible representations of a connected compact Lie group K {\displaystyle K} . The theorem states that there is a bijection
Theorem_of_the_highest_weight
mathematics, a compact semigroup is a semigroup in which the sets of solutions to equations can be described by finite sets of equations. The term "compact" here
Compact_semigroup
Chemical element with atomic number 74 (W)
Tungsten (also called wolfram) is a chemical element; it has symbol W (from German: Wolfram) and atomic number 74. It is a metal found naturally on Earth
Tungsten
Element whose atomic number is greater than 92
the element joliotium (Jl) after Frédéric Joliot-Curie (1965). IUPAC concluded that the JINR had been the first to convincingly synthesize the element (1965)
Transuranium_element
Group that is a topological space with continuous group operations
identity element. Thus every topological group has a neighborhood basis at the identity element consisting of symmetric sets. If G is a locally compact commutative
Topological_group
Chemical element with atomic number 6 (C)
Carbon (from Latin carbo 'coal') is a chemical element; it has symbol C and atomic number 6. It is nonmetallic and tetravalent—meaning that its atoms
Carbon
Numerical method
A discrete element method (DEM), also called a distinct element method, is any of a family of numerical methods for computing the motion and effect of
Discrete_element_method
Chemical element with atomic number 12 (Mg)
Magnesium is a chemical element; it has symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point, and high chemical
Magnesium
Inputs for which a function's value is non-zero
continuous function on a compact topological space has compact support since every closed subset of a compact space is indeed compact. If X {\displaystyle
Support_(mathematics)
Important problem in lattice theory
congruence of an algebra A is finitely generated if and only if it is a compact element of Con A. As every congruence of an algebra is the join of the finitely
Congruence_lattice_problem
Data structure for approximate set membership
requires only about 9.6 bits per element, regardless of the size of the elements. This advantage comes partly from its compactness, inherited from arrays, and
Bloom_filter
Style sheet language
class may apply to any number of instances of any element. An ID may only be applied to a single element. Pseudo-classes are used in CSS selectors to permit
CSS
Theorem in mathematics
equivalent: A {\displaystyle A} is weakly compact. For every f ∈ X ′ , {\displaystyle f\in X^{\prime },} there exists an element a 0 ∈ A {\displaystyle a_{0}\in
James's_theorem
Israeli rock band
Minimal Compact is an Israeli rock band associated with the post-punk movement of the 1980s. Between its foundation in 1980 and its dissolution seven
Minimal_Compact
Mathematical representation in functional analysis
C*-algebra is a locally compact Hausdorff space: In the unital case, i.e. where the C*-algebra has a multiplicative unit element 1, all characters f must
Gelfand_representation
Chemical element with atomic number 5 (B)
Boron is a chemical element; it has symbol B and atomic number 5. In its crystalline form it is a brittle, dark, lustrous metalloid; in its amorphous
Boron
Extinct genus of dinosaurs
and compact element with the three main metatarsals only lacking the first one, in all metatarsals the upper end is slightly eroded. Although compact, the
Hulsanpes
Japanese line of cameras
35 mm film, compact rangefinder camera with a titanium body and Carl Zeiss Sonnar T* 38 mm f/2.8 wide-angle lens. Contax T – with 5-element Carl Zeiss
Contax_T
Markup language for documents
on tr element clear (Obsolete) attribute on br element compact attribute on dl, dir and menu elements type (Deprecated. use CSS instead.), compact (Deprecated
HTML
High density mixed use transit oriented planning
The compact city or city of short distances is an urban planning and urban design concept, which promotes relatively high residential density with mixed
Compact_city
Differentiable manifold
curvature, almost flat spaces arise as quotients of nilmanifolds, and compact nilmanifolds have been used to construct elementary examples of collapse
Nilmanifold
Unicode character block
U+27D0 ⟐ White diamond with centered dot U+27D1 ⟑ And with dot U+27D2 ⟒ Element of opening upward U+27D3 ⟓ Lower right corner with dot U+27D4 ⟔ Upper left
Miscellaneous Mathematical Symbols-A
Miscellaneous_Mathematical_Symbols-A
Product of any collection of compact topological spaces is compact
Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named
Tychonoff's_theorem
Mathematical concept
In mathematics, compact objects, also referred to as finitely presented objects, or objects of finite presentation, are objects in a category satisfying
Compact_object_(mathematics)
Form of abbreviated URI
In computing, a CURIE (or Compact URI) defines a generic, abbreviated syntax for expressing Uniform Resource Identifiers (URIs). It is an abbreviated
CURIE
Compact crossover SUV
The Honda CR-V (also sold as the Honda Breeze in China since 2019) is a compact crossover SUV manufactured by Japanese automaker Honda since 1995. Initial
Honda_CR-V
Association of one output to each input
mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the
Function_(mathematics)
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
each non-compact simple Lie group G, one compact and one non-compact. The non-compact one is a cover of the quotient of G by a maximal compact subgroup
Simple_Lie_group
Duality for locally compact abelian groups
In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups,
Pontryagin_duality
Type of topological group in mathematics
is a locally compact space if and only if the identity element has a compact neighborhood. It follows that there is a local base of compact neighborhoods
Locally_compact_group
Locally compact topological group with an invariant averaging operation
In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant
Amenable_group
Class of mathematical sets
{\displaystyle X} . A Borel subset of X {\displaystyle X} is then simply an element of this σ-algebra. Borel sets are important in measure theory, since any
Borel_set
Axiom of set theory
collection of non-empty sets, one can identify another set containing one element chosen from each set, even if the collection is infinite. Formally, the
Axiom_of_choice
Chemical element with atomic number 61 (Pm)
Promethium is a chemical element; it has symbol Pm and atomic number 61. All of its isotopes are radioactive; it is extremely rare, with only about 500–600
Promethium
Integral transform type in mathematics
Riemannian symmetric space G/K, where G is a Lie group and K is a symmetric compact subgroup. Generalized spheres are then actual geodesic spheres and the
Orbital_integral
Universal identifier for physical object
representations of an EPC identifier, such as the tag-encoding URI format and a compact binary format suitable for storing an EPC identifier efficiently within
Electronic_Product_Code
Chemical element with atomic number 39 (Y)
Yttrium is a chemical element; it has symbol Y and atomic number 39. It is a silvery-metallic transition metal chemically similar to the lanthanides and
Yttrium
Certain topology in mathematics
separable or second-countable [0,ω1] is compact, while [0,ω1) is sequentially compact and countably compact, but not compact or paracompact Any ordinal number
Order_topology
Particular kind of algebraic structure
0 , {\displaystyle 0,} and thus is compact. Moreover, the spectrum σ ( x ) {\displaystyle \sigma (x)} of an element x {\displaystyle x} is non-empty and
Banach_algebra
Wavelet constructed using a spline function
do not have compact supports. There is a certain class of wavelets, unique in some sense, constructed using B-splines and having compact supports. Even
Spline_wavelet
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
Mathematical proposition equivalent to the axiom of choice
Tychonoff's theorem in topology stating that every product of compact spaces is compact, and the theorems in abstract algebra that in a ring with identity
Zorn's_lemma
2025 film by Curry Barker
"so fresh and exhilarating, one can forgive its familiar origins". In Compact, Matthew Schmitz said it defined the genre of "heteropessimist horror"
Obsession_(2025_film)
Multi-sport event in Glasgow, Scotland
Commonwealth Games Council for Scotland issued on 30 August 2024, suggested a compact and low scale Games with 10 sports across four venues including the Scotstoun
2026_Commonwealth_Games
Compaction simulation is the modelling of granular matter when compressed into a dense state that is achieved through the reduction of the air void. The
Compaction_simulation
Chemical element with atomic number 4 (Be)
Beryllium is a chemical element; it has symbol Be and atomic number 4. It is a steel-gray, hard, strong, lightweight and brittle alkaline earth metal
Beryllium
Deformation of the group algebra of a Coxeter group
unimodular locally compact topological group G and a closed subgroup K of G. Then the space of K-biinvariant continuous functions of compact support, Cc(K\G/K)
Iwahori–Hecke_algebra
Device that converts sound into an electrical signal
the Unidyne III capsule to deliver clear and distortion-free sound. Its compact and rugged design allowed it to be put close to drums and amplifiers. It
Microphone
Coordinate system for the Kerr metric
killed in the 1966 University of Texas tower shooting at age 33. The line element for a black hole with a total mass equivalent M {\displaystyle M} , angular
Boyer–Lindquist_coordinates
Family of camera lens
lens, with the f/1.8 being a standard six-element double-Gauss with an air gap and powers between element 2 and 3 and its faster cousins adding additional
Canon_EF_50mm_lens
Hadrosauroid dinosaur genus from the Late Cretaceous
fused neural spines form a compact element, having very thickened and relatively elongated spines. The last sacral element is represented by four fused
Gilmoreosaurus
Maximal compact connected Abelian Lie subgroup
theory of compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups. A torus in a compact Lie group
Maximal_torus
Representation theory
theory of connected compact Lie groups, the proof of the character formula is a key step in proving that every dominant integral element actually arises as
Weyl_character_formula
Term used in composite materials theory
representative elementary volume (REV) (also called the representative volume element (RVE) or the unit cell) is the smallest volume over which a measurement
Representative elementary volume
Representative_elementary_volume
Chemical element with atomic number 13 (Al)
preferred IUPAC name) or aluminum (North American English) is a chemical element; it has symbol Al and atomic number 13. It has a density lower than other
Aluminium
Geological formations in North America
convergent crust boundary. Researchers believe this because the trace element geochemistry of the bentonite shows that its source was a felsic calc-alkalic
Deicke and Millbrig bentonite layers
Deicke_and_Millbrig_bentonite_layers
Compact topological semigroup
with a topology such that S is a compact space and the product is semi-continuous, then S has an idempotent element p, (that is, with pp = p). The lemma
Ellis–Numakura_lemma
Algebraic construct of interest in theoretical physics
Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras)
Quantum_group
Mathematical concept
vector space weakly closed (respectively, weakly compact, etc.) if they are closed (respectively, compact, etc.) with respect to the weak topology. Likewise
Weak_topology
Attribute of a geometric shape
definitions to aspect ratios of general compact sets in a d-dimensional space: The diameter-width aspect ratio (DWAR) of a compact set is the ratio of its diameter
Aspect_ratio
Abstract structure in mathematics
In mathematics, compact quantum groups are generalisations of compact groups, where the commutative C ∗ {\displaystyle \mathrm {C} ^{*}} -algebra of continuous
Compact_quantum_group
identity element contains a compact open subgroup. Equivalently, a locally profinite group is a topological group that is Hausdorff, locally compact, and
Locally_profinite_group
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
Chemical element with atomic number 41 (Nb)
Niobium is a chemical element; it has symbol Nb (formerly columbium, Cb) and atomic number 41. It is a light grey, crystalline transition metal. Pure
Niobium
In mathematics, a regular element of a Lie algebra or Lie group is an element whose centralizer has dimension as small as possible. For example, in a
Regular element of a Lie algebra
Regular_element_of_a_Lie_algebra
Class of electronic filter
advantage of being very compact, but the low quality factor of the resonators leads to relatively poor performance. Lumped-element LC filters have both an
RF_and_microwave_filter
Elongated cell in the phloem tissue of flowering plants
companion cells and sieve elements), the network of companion cells with the compact sieve tubes was highlighted. The markers for sieve elements and companion
Sieve_tube_element
Set with associative invertible operation
third element within the same set and the following conditions must hold: the operation is associative, it has an identity element, and every element of
Group_(mathematics)
Transformations induced by a mathematical group
an operation that takes an element of G {\displaystyle G} and an element of S {\displaystyle S} and produces another element of S . {\displaystyle S.}
Group_action
Electrical circuit with equal-length transmission lines
to design distributed-element filters. Such filters constructed directly by Richards' and Kuroda's method are not very compact. This can be an important
Commensurate_line_circuit
Microscopic optical resolution test device
elements; thus there are 54 target elements provided in the full series. Each element consists of three bars which form a minimal Ronchi ruling. These 54 elements
1951 USAF resolution test chart
1951_USAF_resolution_test_chart
COMPACT ELEMENT
COMPACT ELEMENT
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.
Boy/Male
Hindu, Indian
Compact; Firm; Solid
Boy/Male
Hindu, Indian, Sanskrit
Company
Boy/Male
Indian, Punjabi, Sikh
Liberation through Company
Boy/Male
Hindu, Indian
Compact; Safe; Secure
Boy/Male
Indian, Punjabi, Sikh
Company of Guru
Boy/Male
Indian, Sanskrit
Fallen from Glory
Boy/Male
Hindu, Indian, Sanskrit
In the Company
Girl/Female
Indian, Telugu
Good Company
Girl/Female
Arabic, Muslim
Beauty of Company
Boy/Male
Indian, Punjabi, Sikh
Good Company
Boy/Male
Indian, Punjabi, Sikh
Lord's Company
Girl/Female
Arabic, Muslim
Beauty of 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.
Girl/Female
Tamil
Compare
Girl/Female
Hindu, Indian
Compare
Girl/Female
Arabic
Sensible Contact
Boy/Male
Indian, Tamil
No Compare
Girl/Female
Hindu, Indian, Marathi, Tamil
Compact; Promise
Girl/Female
Muslim
Beauty of company
COMPACT ELEMENT
COMPACT ELEMENT
Boy/Male
Hindu, Indian, Malayalam, Marathi
Sweet; Friend
Surname or Lastname
English
English : habitational name from a lost or unidentified place, possibly in Lancashire, where the surname is most frequent.
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit
Glorious
Boy/Male
Muslim/Islamic
Crown
Boy/Male
Hindu
One who likes being merciful, A king
Boy/Male
Hindu, Indian, Kannada, Marathi, Telugu
Prosperous
Girl/Female
Indian, Tamil
Desirable as the Moon; Life
Boy/Male
Tamil
Lord of the world, Homeless, Lord Shiva, Lord of all
Girl/Female
British, English, Hebrew, Irish
Rhyming Variant of Molly; Bitterness; Star of the Sea; Small
Boy/Male
English
Made of Oak
COMPACT ELEMENT
COMPACT ELEMENT
COMPACT ELEMENT
COMPACT ELEMENT
COMPACT ELEMENT
n.
One who makes a compact.
n.
Extent; reach; sweep; capacity; sphere; as, the compass of his eye; the compass of imagination.
n.
An inclosing limit; boundary; circumference; as, within the compass of an encircling wall.
adv.
In a compact manner; with close union of parts; densely; tersely.
n.
Guests or visitors, in distinction from the members of a family; as, to invite company to dine.
v. t.
To compact or join anew.
v. i.
To bear or endure; to put up (with); as, to comport with an injury.
a.
Strong; firm; compact.
v. i.
To be like or equal; to admit, or be worthy of, comparison; as, his later work does not compare with his earlier.
a.
Compact; pressed close; concentrated; firmly united.
n.
The crew of a ship, including the officers; as, a whole ship's company.
v. t.
To mingle, as different fertilizing substances, in a mass where they will decompose and form into a compost.
p. p. & a
Brief; close; pithy; not diffuse; not verbose; as, a compact discourse.
imp. & p. p.
of Compact
v. t.
To manure with compost.
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.
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.
n.
Contact or impression by touch; collision; forcible contact; force communicated.
p. pr. & vb. n.
of Compact