• observed in experiments. Compactification is one way of modifying the number of dimensions in a physical theory. In compactification, some of the extra dimensions...
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  • Projectively extended real line Stone–Čech compactification Stone topology Stone–Čech remainder Wallman compactification This lists named topologies of uniform...
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    compactification of it. But there are other ways to compactify D / Γ {\displaystyle D/\Gamma } ; for example, there is the minimal compactification of...
    41 KB (5,761 words) - 09:09, 9 October 2024
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    compactification. The one-point compactification of R {\displaystyle \mathbb {R} } is homeomorphic to the circle S1; the one-point compactification of...
    45 KB (5,697 words) - 16:35, 12 November 2024
  • One can also arrange that W is integral if X is integral. Nagata's compactification theorem, as generalized by Deligne, says that a separated morphism...
    18 KB (2,834 words) - 09:35, 16 December 2024
  • 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...
    15 KB (2,023 words) - 20:13, 19 October 2024
  • {\displaystyle \beta _{j}} that are coming from the first homology of the compactification of each of the components. The one-cycle in X k ⊂ X {\displaystyle...
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  • Thumbnail for Armand Borel
    theorem Borel–de Siebenthal theory Borel–Moore homology Baily–Borel compactification Linear algebraic group Spin structure Borel, Armand (1960), Seminar...
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  • {\displaystyle X} as a dense subset of a compact space is called a compactification of X . {\displaystyle X.} A linear operator between topological vector...
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  • the one-point compactification of X {\displaystyle X} is a perfect, compact Hausdorff space. Therefore, the one point compactification of X {\displaystyle...
    17 KB (2,667 words) - 01:59, 28 December 2024
  • Revêtements étales et groupe fondamental - (SGA 1) (Documents Mathématiques 3), Paris: Société Mathématique de France, pp. xviii+327, see Exp. V, IX, X, arXiv:math...
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  • In mathematics, an Eells–Kuiper manifold is a compactification of R n {\displaystyle \mathbb {R} ^{n}} by a sphere of dimension n / 2 {\displaystyle n/2}...
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  • Busemann functions by constants. Eberlein & O'Neill (1973) defined a compactification of a Hadamard manifold X which uses Busemann functions. Their construction...
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  • method for compactification of C n {\displaystyle \mathbb {C} ^{n}} , but not the only method like the Riemann sphere that was compactification of C {\displaystyle...
    124 KB (17,684 words) - 19:46, 25 October 2024
  • Rf_{!}:=Rp_{*}j_{!}} where f = p ∘ j {\displaystyle f=p\circ j} is a compactification of f, i.e., a factorization into an open immersion followed by a proper...
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  • Grothendieck school would see it); but geometrically it is more like a compactification question, as the stability criteria revealed. The restriction to non-singular...
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  • scheme that is not connected is Spec(k[x]×k[x]) compactification See for example Nagata's compactification theorem. Cox ring A generalization of a homogeneous...
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  • affine scheme whose underlying topological space is the Stone–Čech compactification of the positive integers (with the discrete topology). In fact, the...
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    string, the Spin(32)/Z2 heterotic string, and M-theory are related by compactification on a K3 surface. For example, the Type IIA string compactified on a...
    34 KB (5,241 words) - 11:35, 23 November 2024
  • Thumbnail for Tropical geometry
    tropological (Carrollian) sigma models. Tropical analysis Tropical compactification Hartnett, Kevin (5 September 2018). "Tinkertoy Models Produce New Geometric...
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  • Thumbnail for Hillel Furstenberg
    surfaces in the early 1970s. The Furstenberg boundary and Furstenberg compactification of a locally symmetric space are named after him, as is the Furstenberg–Sárközy...
    16 KB (1,470 words) - 12:39, 7 December 2024
  • Thumbnail for Holonomy
    Most important are compactifications on Calabi–Yau manifolds with SU(2) or SU(3) holonomy. Also important are compactifications on G2 manifolds. Computing...
    42 KB (5,901 words) - 15:27, 22 November 2024
  • the supervision of Oscar Zariski, with a thesis "Ultrafilters and Compactification of Uniform Spaces". Samuel ran a Paris seminar during the 1960s, and...
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  • Thumbnail for Quasi-isometry
    Adding a point at each end yields a compactification of the original space, known as the end compactification. The ends of a finitely generated group...
    15 KB (2,392 words) - 11:02, 3 December 2023
  • S2CID 11437903. Hindman, Neil; Strauss, Dona (1998). Algebra in the Stone-Čech compactification : theory and applications. New York: Walter de Gruyter. ISBN 311015420X...
    6 KB (738 words) - 14:49, 23 October 2024
  • is surjective if q = 2n - 1. Fulton–MacPherson compactification The Fulton–MacPherson compactification of the configuration space of n distinct labeled...
    52 KB (7,621 words) - 14:44, 11 November 2024
  • irreducibility of the space of curves of given genus" (PDF). Publications Mathématiques de l'IHÉS. 36: 75–109. CiteSeerX 10.1.1.589.288. doi:10.1007/bf02684599...
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  • basic spaces tend to be unwieldy – the projective line over Cp is a compactification of the inductive limit of affine Bruhat–Tits buildings for PGL2(F)...
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  • Thumbnail for G2 (mathematics)
    Montgomery (2009). "G2 and the "rolling distribution"". L'Enseignement Mathématique. 55: 157–196. arXiv:math/0612469. doi:10.4171/lem/55-1-8. S2CID 119679882...
    15 KB (2,056 words) - 18:40, 24 July 2024
  • Euclidean space is Euclidean space, which shows that A is the 1-point compactification of Euclidean space and therefore A is homeomorphic to the n-sphere...
    9 KB (1,099 words) - 05:20, 23 January 2022