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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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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)
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
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
{\overline {\mathcal {T}}}} is compact: it is called the Thurston compactification of the Teichmüller space. The boundary T ¯ ∖ T {\displaystyle {\overline
Thurston_boundary
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
a compactification of cubic fourfolds with ADE singularities (including all smooth cubic fourfolds). He further showed that this compactification is
Cubic_fourfold
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
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
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
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
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
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
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
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)
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
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
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
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
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 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
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
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
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
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
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
South African mathematician
Mathematician Neil Hindman, with whom Strauss wrote a book on the Stone–Čech compactification of topological semigroups, has stated the following as advice for other
Dona_Strauss
Jean-Pierre Serre, a French mathematician. Bass–Serre theory Borel-Serre Compactification Grothendieck-Serre Correspondence Serre class Quillen–Suslin theorem
List of things named after Jean-Pierre Serre
List_of_things_named_after_Jean-Pierre_Serre
Five-dimensional Einstein field equations
{\displaystyle \square \phi =0.} Through the process of Kaluza–Klein compactification, the additional extra dimension is rolled up in a circle. Hence spacetime
Kaluza–Klein–Einstein field equations
Kaluza–Klein–Einstein_field_equations
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
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
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
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.
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
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
Class of mathematical expression
\}} is the projectively extended real line, which is a one-point compactification of the real line. Here ∞ {\displaystyle \infty } means an unsigned
Division_by_zero
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
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
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)
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
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
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
Type of topological space
two-point spaces, and a dyadic space is a topological space with a compactification which is a dyadic compactum. However, many authors use the term dyadic
Dyadic_space
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
"non-degenerate" way. It is the noncommutative generalization of Stone–Čech compactification. Multiplier algebras were introduced by Busby (1968). For example,
Multiplier_algebra
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
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)
Study of angle-preserving transformations of a geometric space
space with a null cone added at infinity". That is, the setting is a compactification of a familiar space; the geometry is concerned with the implications
Conformal_geometry
Mapping equal to its square under mapping composition
projected point for P. The correspondence makes the sphere a one-point compactification for the plane when a point at infinity is included to correspond to
Projection_(mathematics)
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
Algebraic variety
be used to refer to the compactified modular curves X(Γ) which are compactifications obtained by adding finitely many points (called the cusps of Γ) to
Modular_curve
{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
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
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
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
enriched over [ 0 , ∞ ] {\displaystyle [0,\infty ]} , the one-point compactification of R {\displaystyle \mathbb {R} } . The notion was introduced in 1973
Generalized_metric_space
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
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
Principle in theoretical physics
string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold Ricci-flat manifold Calabi–Yau manifold
Holographic_principle
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
Physicist
gravity. Becker's work included developing models for superstring compactification and, working with her sister Katrin Becker, she developed one for the
Melanie_Becker
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
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
Topics referred to by the same term
theorem characterizes when a topological space is metrizable Nagata's compactification theorem, an algebraic formula Nagata's conjecture, an algebraic formula
Nagata
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
In geometry, a tame manifold is a manifold with a well-behaved compactification. More precisely, a manifold M {\displaystyle M} is called tame if it is
Tame_manifold
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
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
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
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
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
British mathematician
algebraic geometry, such as: singularities in the minimal model program; compactification of moduli spaces; the rationality of orbit spaces, including the moduli
Nicholas_Shepherd-Barron
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
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
Professor of mathematics (born 1969)
his PhD from Harvard University in 1994 with a thesis entitled `A Compactification over the Moduli Space of Stable Curves of the Universal Moduli Space
Rahul_Pandharipande
Theorem of physical impossibility
theorem. Goddard–Thorn theorem Maldacena–Nunez no-go theorem: any compactification of type IIB string theory on an internal compact space with no brane
No-go_theorem
Extra-dimensional model of the universe
83.3370. Randall, Lisa; Sundrum, Raman (1999). "An Alternative to Compactification". Physical Review Letters. 83 (23): 4690–4693. arXiv:hep-th/9906064
Randall–Sundrum_model
Argument in string theory
dimensions rolled up in Planck scale, as described by Kaluza–Klein compactification. In simple terms, the argument connected with brane cosmology claims
Brandenberger–Vafa_mechanism
Hypothetical particle
dimensions varies. It appears as a radion in Kaluza–Klein theory's compactifications of extra dimensions. In Brans–Dicke theory of gravity, Newton's constant
Dilaton
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
Mathematical theory
such singularities can be handled rather as a (complicated) sort of compactification, ending up with a compact manifold (for the strong topology, rather
Singularity_theory
COMPACTIFICATION
COMPACTIFICATION
COMPACTIFICATION
COMPACTIFICATION
Male
English
Variant spelling of English Harvey, HARVIE means "battle worthy."
Girl/Female
Hindu, Indian
Origin of Soul
Girl/Female
British, English
Female Version of Blair; Flatland
Boy/Male
Australian, French, Swedish
He who Seduces
Surname or Lastname
English
English : habitational name from one of three places in Lincolnshire: Aunby, Owmby, and Aunsby, all of which are named with the Old Norse personal name Auðun + býr ‘farmstead’, ‘settlement’.
Girl/Female
Gujarati, Hindu, Indian, Sanskrit
Desire
Boy/Male
Tamil
Atulya | அதà¯à®²à¯à®¯à®¾
Unequalled, Unrivalled, Immeasurable, Unique, Unweigh able, Incomparable
Male
French
French name derived from Latin Dio, a short form of longer names of Greek origin beginning with Dio-, DION means "Zeus."
Girl/Female
Hindu, Indian, Japanese, Kannada, Malayalam, Marathi, Sindhi, Swedish, Telugu
Smaller; Little One; Bold
Boy/Male
Slavic
Victorious; conquerer of the people.
COMPACTIFICATION
COMPACTIFICATION
COMPACTIFICATION
COMPACTIFICATION
COMPACTIFICATION