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Topics referred to by the same term
Look up compactification in Wiktionary, the free dictionary. Compactification may refer to: Compactification (mathematics), making a topological space
Compactification
Mathematical concept
In algebraic geometry, a tropical compactification is a compactification (projective completion) of a subvariety of an algebraic torus, introduced by Jenia
Tropical_compactification
Technique in theoretical physics
In theoretical physics, compactification means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with this
Compactification_(physics)
Concept in topology
adding points so that certain kinds of limits exist. The Stone–Čech compactification of a space provides the most extensive such enlargement: it adds enough
Stone–Čech_compactification
In mathematics, the Bohr compactification of a topological group G is a compact Hausdorff topological group H that may be canonically associated to G.
Bohr_compactification
Embedding a topological space into a compact space as a dense subset
In mathematics, in general topology, compactification is the process or result of making a topological space into a compact space. A compact space is a
Compactification (mathematics)
Compactification_(mathematics)
wonderful compactification of a variety acted on by an algebraic group G {\displaystyle G} is a G {\displaystyle G} -equivariant compactification such that
Wonderful_compactification
In mathematics, the Baily–Borel compactification is a compactification of a quotient of a Hermitian symmetric space by an arithmetic group, introduced
Baily–Borel_compactification
Way to extend a non-compact topological space
is called the one-point compactification or Alexandroff compactification. The advantages of the Alexandroff compactification lie in its simple, often
Alexandroff_extension
Parametrizes complex structures on a surface
continuous action on this compactification. Gardiner & Masur (1991) considered a compactification similar to the Thurston compactification, but using extremal
Teichmüller_space
A compactification of T1 topological spaces
In mathematics, the Wallman compactification, generally called Wallman–Shanin compactification is a compactification of T1 topological spaces that was
Wallman_compactification
In algebraic geometry, Nagata's compactification theorem, introduced by Nagata (1962, 1963), implies that every abstract variety can be embedded in a complete
Nagata's compactification theorem
Nagata's_compactification_theorem
Configuration space
In geometry, the Fulton–MacPherson compactification of the configuration space of n distinct labeled points in a compact complex manifold is a compact
Fulton–MacPherson compactification
Fulton–MacPherson_compactification
Supergravity in eleven dimensions
Kaluza–Klein compactification made it hard to acquire chiral fermions needed to build the Standard Model. Additionally, these compactifications generally
Eleven-dimensional supergravity
Eleven-dimensional_supergravity
Framework of superstring theory
observed in experiments. Compactification is one way of modifying the number of dimensions in a physical theory. In compactification, some of the extra dimensions
M-theory
Adding a point at each end yields a compactification of the original space, known as the end compactification. The notion of an end of a topological
End_(topology)
Riemannian manifold with SU(n) holonomy
supercharges in a compactification of type IIA supergravity or 2 5 − n {\displaystyle 2^{5-n}} supercharges in a compactification of type I. When fluxes
Calabi–Yau_manifold
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
physics based on string theory, this is accomplished by a process called compactification, in which the extra dimensions are assumed to "close up" on themselves
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Concept of mathematics in convex analysis
mathematics, specifically in convex analysis, the convex compactification is a compactification which is simultaneously a convex subset in a locally convex
Convex_compactification
the always compact Seiberg–Witten moduli space, with made laborious compactifications using Uhlenbeck's compactness theorem required for Donaldson invariants
Donaldson_invariant
Theory of strings with supersymmetry
occurring as a result of a Kaluza–Klein compactification of 11D M-theory that contains membranes. Because compactification of a geometric theory produces extra
Superstring_theory
Concept in geometry
Thus, the circle is the one-point compactification of the real line, and the sphere is the one-point compactification of the plane. Projective spaces Pn
Point_at_infinity
Theory of subatomic structure
observed in experiments. Compactification is one way of modifying the number of dimensions in a physical theory. In compactification, some of the extra dimensions
String_theory
a compactification of cubic fourfolds with ADE singularities (including all smooth cubic fourfolds). He further showed that this compactification is
Cubic_fourfold
Boundary region of asymptotically flat spacetimes in general relativity
{\displaystyle ds^{2}=-dt^{2}+dr^{2}+r^{2}d\Omega ^{2}} . Conformal compactification induces a transformation which preserves angles, but changes the local
Null_infinity
Type of topological space in mathematics
cannot be a neighbourhood of any point in Hilbert space. The one-point compactification of the rational numbers Q is compact and therefore locally compact
Locally_compact_space
Mathematical object
with these properties. The 3-sphere is homeomorphic to the one-point compactification of R3. In general, any topological space that is homeomorphic to the
3-sphere
Namikawa, Yukihiko (1980). "Main problem and main results". Toroidal Compactification of Siegel Spaces. Lecture Notes in Mathematics. Vol. 812. Springer
List of letters used in mathematics, science, and engineering
List_of_letters_used_in_mathematics,_science,_and_engineering
Objects in eleven-dimensional supergravity
Supermembranes are hypothesized objects that live in the 11-dimensional theory called M-Theory and should also exist in eleven-dimensional supergravity
Supermembranes
Form of dimensional reduction
Freund–Rubin compactification is a form of dimensional reduction in which a field theory in d-dimensional spacetime, containing gravity and some field
Freund–Rubin_compactification
Mathematical object studied in the field of algebraic geometry
moduli of curves, a compactification of a moduli need not be unique and, in some cases, different non-equivalent compactifications are constructed using
Algebraic_variety
Set of mathematical concepts in quantum gravity
needed for computation. By utilizing compactifications, string theory describes geometric states, where a compactification is a spacetime that looks four-dimensional
Quantum_geometry
Unified field theory
to obtain a higher-dimensional manifold is referred to as compactification. Compactification does not produce group actions on chiral fermions except in
Kaluza–Klein_theory
Collection of possible string theory vacua
comprising a collective "landscape" of choices of parameters governing compactifications. The term "landscape" comes from the notion of a fitness landscape
String_theory_landscape
Czech mathematician (1893–1960)
topology. He is especially known for the technique known as Stone–Čech compactification (in topology) and the notion of Čech cohomology. He was the first to
Eduard_Čech
Generalization of a manifold
like cones over a certain base. In physics, in particular in flux compactifications of string theory, the base is usually a five-dimensional real manifold
Conifold
Soviet mathematician (1896–1982)
contributions to set theory and topology. In topology, the Alexandroff compactification and the Alexandrov topology are named after him. Alexandrov attended
Pavel_Alexandrov
Space of complex matrices with positive definite imaginary part
familiar compactification of modular curves by adding cusp points. A finer class of compactifications is given by toroidal compactifications, which depend
Siegel_upper_half-space
Concept in mathematics
ISSN 0022-2488. Fulton, William; MacPherson, Robert (January 1994). "A Compactification of Configuration Spaces". Annals of Mathematics. 139 (1): 183. doi:10
Configuration space (mathematics)
Configuration_space_(mathematics)
Certain topology in mathematics
Stone–Čech compactification of ω1 is ω1+1, just as its one-point compactification (in sharp contrast to ω, whose Stone–Čech compactification is much larger
Order_topology
{\overline {\mathcal {T}}}} is compact: it is called the Thurston compactification of the Teichmüller space. The boundary T ¯ ∖ T {\displaystyle {\overline
Thurston_boundary
Type of mathematical space
compactification. The one-point compactification of R {\displaystyle \mathbb {R} } is homeomorphic to the circle S1; the one-point compactification of
Compact_space
Type of topological space
space similar to the space of non-isolated points of the Stone–Čech compactification of the integers. A Parovicenko space is a topological space X satisfying
Parovicenko_space
In algebraic geometry, the smooth completion (or smooth compactification) of a smooth affine algebraic curve X is a complete smooth algebraic curve which
Smooth_completion
compact type as a compactification of a finite-dimensional complex semisimple Jordan algebra. The automorphism group of the compactification becomes a complex
Mutation_(Jordan_algebra)
Line formed by the real numbers
and the resulting end compactification is the extended real number line [−∞, +∞]. There is also the Stone–Čech compactification of the real line, which
Number_line
Mathematical functions of split-complex numbers
fractional transformations as bijections on the projective line a compactification of D is used. See the section given below. The exponential function
Motor_variable
Type of matrix barcode
Extended Channel Interpretation support. Han Xin code has special compactification mode for URI encoding and can reduce barcode size which encodes links
Han_Xin_code
Branch of string theory
referred to as the string theory landscape may be dominated by F-theory compactifications on Calabi–Yau four-folds, with 10 272 , 000 {\displaystyle 10^{272
F-theory
Relationship between two functors abstracting many common constructions
free group on a set in algebra, or the construction of the Stone–Čech compactification of a topological space in topology. By definition, an adjunction between
Adjoint_functors
so, for g in X, k(g) = g(x1). Hence the correspondence between the compactifications for x0 and x1 is given by sending g in X(x0) to g + g(x1)1 in X(x1)
Busemann_function
American mathematician (1930–2013)
was with Armand Borel, now known as the Baily–Borel compactification, which is a compactification of a quotient of a Hermitian symmetric space by an arithmetic
Walter_Lewis_Baily_Jr.
Function that "converges" to periodicity
functions are essentially the same as continuous functions on the Bohr compactification of the reals. The space Sp of Stepanov almost periodic functions (for
Almost_periodic_function
"non-degenerate" way. It is the noncommutative generalization of Stone–Čech compactification. Multiplier algebras were introduced by Busby (1968). For example,
Multiplier_algebra
Japanese mathematician
geometry, earning him the nickname "Mr. Counterexample". Nagata's compactification theorem shows that algebraic varieties can be embedded in complete
Masayoshi_Nagata
Mathematical model of the time dependence of a point in space
useful to study the continuous extension Φ* of Φ to the one-point compactification X* of X. Even after losing the differential structure of the original
Dynamical_system
Homology theory for locally compact spaces
relative homology Hi(Y, S). Under the same assumption on X, the one-point compactification of X is homeomorphic to a finite CW complex. As a result, Borel–Moore
Borel–Moore_homology
One-dimensional complex manifold
algebraic curve. Every elliptic curve is an algebraic curve, given by (the compactification of) the locus y 2 = x 3 + a x + b {\displaystyle y^{2}=x^{3}+ax+b}
Riemann_surface
Japanese mathematician
completing his doctoral dissertation, titled "The geometry of the compactification of the Hurwitz scheme," also under the supervision of Faltings. After
Shinichi_Mochizuki
Duality for locally compact abelian groups
to characterize the Bohr compactification of an arbitrary abelian locally compact topological group. The Bohr compactification B ( G ) {\displaystyle B(G)}
Pontryagin_duality
Theories in particle physics and cosmology
string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold Ricci-flat manifold Calabi–Yau manifold
Brane_cosmology
2D surface which extends indefinitely
hypersurface in three-dimensional Minkowski space.) The one-point compactification of the plane is homeomorphic to a sphere (see stereographic projection);
Plane_(mathematics)
Topology in mathematics
corona set, is the complement βX \ X of the space in its Stone–Čech compactification βX. A topological space is said to be σ-compact if it is the union
Stone–Čech_remainder
French physicist (1942–2019)
eleven-dimensional supergravity theory and proposed a mechanism of spontaneous compactification in field theory. He was also one of the first to write down the full
Eugène_Cremmer
Topological space in mathematics
long ray, L ∗ , {\displaystyle L^{*},} is obtained as the one-point compactification of L {\displaystyle L} by adjoining an additional element to the right
Long_line_(topology)
American theoretical physicist and professor (born 1970)
particle theory. He has made central contributions to the study of compactifications of string theory from ten to four dimensions, especially in the investigation
Shamit_Kachru
Continuous deformation between two continuous functions
homology (which is, roughly speaking, the homology of the compactification, and compactification is not homotopy invariant). In order to define the fundamental
Homotopy
Partial differential equations whose solutions are instantons
representation of the field strength of a BPST instanton with center z on the compactification S4 of R4 (bottom right). The BPST instanton is a solution to the anti-self
Yang–Mills_equations
Type of regular Hausdorff space
Hausdorff compactification. Among those Hausdorff compactifications, there is a unique "most general" one, the Stone–Čech compactification β X . {\displaystyle
Tychonoff_space
Mathematical concept
the topological space of the real numbers, producing the two-point compactification of the real numbers. Adding algebraic properties to this gives us the
Infinity
Property of a differential manifold that includes complex structures
a leading role in physical string theory, as supersymmetric flux compactifications, which relate 10-dimensional physics to 4-dimensional worlds like
Generalized_complex_structure
Type of topological space
space underlying any profinite group is a Stone space. The Stone–Čech compactification of the natural numbers with the discrete topology, or indeed of any
Stone_space
{C} } in order to render it compact (in this case it is a one-point compactification). This space denoted C ^ {\displaystyle {\hat {\mathbb {C} }}} is isomorphic
Residue_at_infinity
Compact astronomical body
string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold Ricci-flat manifold Calabi–Yau manifold
Black_hole
particularly simple formula for certain integrals on the Deligne–Mumford compactification M ¯ g , n {\displaystyle {\overline {\mathcal {M}}}_{g,n}} of the moduli
Lambda_g_conjecture
Taiwanese mathematician
mathematics from Harvard University in 1984. His doctoral thesis, Compactification of the Siegel Moduli Schemes, was completed under the supervision of
Ching-Li_Chai
Quantum field theory
representation of the field strength of a BPST instanton with center z on the compactification S4 of ℝ4 (bottom right). The BPST instanton is a classical instanton
Yang–Mills_theory
topology Cocountable topology Cofinite topology Compact-open topology Compactification Discrete topology Double-pointed cofinite topology Extended real number
List of examples in general topology
List_of_examples_in_general_topology
Topological space defined by the union of circles
space H {\displaystyle \mathbb {H} } is homeomorphic to the one-point compactification of the union of a countable family of disjoint open intervals. The
Hawaiian_earring
Ten-dimensional supergravity
equations of motion. It is acquired by a compactification of eleven-dimensional MM theory on a circle. Compactification of eleven-dimensional supergravity on
Type_IIA_supergravity
Strong-weak duality in supersymmetric theories of theoretical physics
string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold Ricci-flat manifold Calabi–Yau manifold
Montonen–Olive_duality
Type of matrix barcode
in mixed mode which is a combination of existing modes for better compactification or special selectors like ECI designator. Every compaction mode depends
Rectangular_Micro_QR_Code
2023 Chinese science fiction television series
hence elementary particles, for which eleven dimensions exist due to compactification, can have enormous complexity. Ding Yi assumes that the Trisolarans
Three-Body
In mathematics, the prime end compactification is a method to compactify a topological disc (i.e. a simply connected open set in the plane) by adding the
Prime_end
Pathological embedding of the sphere in 3D space
sphere as an embedding into the 3-sphere, considered as the one-point compactification of the 3-dimensional Euclidean space R3. The closure of the non-simply
Alexander_horned_sphere
Singularity theorem in Yang–Mills theory
space arise from Yang–Mills fields on the curved sphere, its one-point compactification. The theorem is named after Karen Uhlenbeck, who first described it
Uhlenbeck's singularity theorem
Uhlenbeck's_singularity_theorem
Space which has no holes through it
{\displaystyle \operatorname {SU} (n)} is simply connected. The one-point compactification of R {\displaystyle \mathbb {R} } is not simply connected (even though
Simply_connected_space
Romanian-American physicist (1936–2018)
Two-component duality Higher-dimensional unification Freund–Rubin compactification Superstrings from 26 dimensions p-adic strings econophysics Spouse
Peter_Freund
Generalized sphere of dimension n (mathematics)
stereographic projection, the n {\displaystyle n} -sphere is the one-point compactification of n {\displaystyle n} -space. The n {\displaystyle n} -spheres
N-sphere
French mathematician (1921–2009)
the supervision of Oscar Zariski, with a thesis "Ultrafilters and Compactification of Uniform Spaces". Samuel ran a Paris seminar during the 1960s, and
Pierre_Samuel
Type of Yang–Mills instanton
around z=0 (bottom left). A visual representation of the field strength of a BPST instanton with center z on the compactification S4 of R4 (bottom right).
BPST_instanton
Type of topological space
continuous function of a topological power of an Alexandroff one-point compactification of a discrete space. Polyadic spaces were first studied by S. Mrówka
Polyadic_space
Black brane solution in eleven-dimensional supergravity
The M5-brane is the electric-magnetic dual of the M2-brane. Upon compactification, the M5-brane becomes either the D4-brane or the NS5-brane of type
M5-brane
American Internet personality and musician (born 1975)
in string theory and supersymmetry: a-maximization, nongeometric compactifications, and tachyon cosmology (2004) Doctoral advisor Kenneth A. Intriligator
Brian_Wecht
American mathematician
he published two papers setting out what is now called Stone–Čech compactification theory. This theory grew out of his attempts to understand more deeply
Marshall_H._Stone
Concept in particle physics
at an energy scale that is directly related to the inverse size ("compactification scale") of the extra dimension, M KK ≈ R − 1 . {\displaystyle M_{\text{KK}}\approx
Universal_extra_dimensions
Theories of higher-dimensional general relativity
often confined to lower-dimensional hypersurfaces known as branes. Compactification mechanisms, such as Calabi–Yau manifolds in string theory, reduce the
Higher-dimensional Einstein gravity
Higher-dimensional_Einstein_gravity
French mathematician
contribution by Lafforgue to solve this question is the construction of compactifications of certain moduli stacks of shtukas. The proof was the result of more
Laurent_Lafforgue
List of concrete topologies and topological spaces
topology Weak topology Compactifications include: Alexandroff extension Projectively extended real line Bohr compactification Eells–Kuiper manifold Projectively
List_of_topologies
Type of topological space
compact Hausdorff spaces are normal; In particular, the Stone–Čech compactification of a Tychonoff space is normal Hausdorff; Generalizing the above examples
Normal_space
COMPACTIFICATION
COMPACTIFICATION
COMPACTIFICATION
COMPACTIFICATION
Girl/Female
Arabic, Hindu, Indian, Muslim
Forgiver; One who Forgives
Boy/Male
Gaelic
Lives near the clear stream.
Boy/Male
Scandinavian Latin
Boy/Male
Australian, Christian, Teutonic
Surname and Place Name; The House of Windsor has been the Ruling Family of the Uk Since 1917; From Windsor; Landing Place with a Windlass
Male
Egyptian
, a mystical title of the deity Amen Ra.
Girl/Female
Hindu
Famous, Successful
Boy/Male
Hindu
Warrior
Surname or Lastname
English
English : from an Old French personal name Amand, Amant (from Latin Amandus meaning ‘loveable’).German : variant spelling of Amend.
Surname or Lastname
English
English : occupational name for a peasant farmer, from Middle English husband ‘tiller of the soil’, ‘husbandman’. The term (late Old English hūsbonda, Old Norse húsbóndi), a compound of hús ‘house’ + bóndi (see Bond) originally described a man who was head of his own household, and this may have been the sense in some of the earliest examples of the surname.
Surname or Lastname
English
English : unexplained. Perhaps a variant of Scottish Nevins.
COMPACTIFICATION
COMPACTIFICATION
COMPACTIFICATION
COMPACTIFICATION
COMPACTIFICATION