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There is a page named "Continuous functions on a compact Hausdorff space" on Wikipedia
- especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space X {\displaystyle X} with values...7 KB (1,108 words) - 22:17, 15 December 2022
- limits in the first place). The algebra of continuous (real or complex) functions on a compact Hausdorff space is a commutative C*-algebra, and conversely...16 KB (2,163 words) - 10:32, 20 August 2024
- topological space X. If X is locally compact and Hausdorff, such functions are precisely those extendable to a continuous function g on its one-point...19 KB (2,531 words) - 15:27, 24 December 2023
such that A ⊆ U and B ⊆ V. A continuous bijection from a compact space into a Hausdorff space is a homeomorphism. A compact Hausdorff space is normal...45 KB (5,681 words) - 09:54, 31 July 2024- continuous functions on a compact Hausdorff space. Further, there is a generalization of the Stone–Weierstrass theorem to noncompact Tychonoff spaces...27 KB (3,234 words) - 20:46, 8 June 2024
- Arzelà–Ascoli theorem (category Theory of continuous functions)sufficient conditions for a family of functions from a compactly generated Hausdorff space into a uniform space to be compact in the compact-open topology; see...27 KB (3,817 words) - 22:11, 21 May 2024
- a C*-subalgebra of some B ( H ) . {\displaystyle B(H).} The space C ( K ) {\displaystyle C(K)} of complex continuous functions on a compact Hausdorff...103 KB (17,213 words) - 23:33, 24 August 2024
Uniform continuity (redirect from Uniformly continuous functions)topology. A consequence is a generalization of the Heine-Cantor theorem: each continuous function from a compact Hausdorff space to a uniform space is uniformly...25 KB (4,148 words) - 04:48, 19 August 2024- Equicontinuity (category Theory of continuous functions)analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood, in a precise...25 KB (3,745 words) - 22:02, 7 June 2023
- interval onto the unit square (any continuous bijection from a compact space onto a Hausdorff space is a homeomorphism). But a unit square has no cut-point...15 KB (1,957 words) - 01:18, 7 August 2024
- continuous functions. Such a topology is called a vector topology and every topological vector space has a uniform topological structure, allowing a notion...103 KB (13,529 words) - 03:12, 5 July 2024
- called a homeomorphism. If a continuous bijection has as its domain a compact space and its codomain is Hausdorff, then it is a homeomorphism. Given a function...60 KB (9,404 words) - 23:34, 13 August 2024
- by Dieudonné (1944). Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a Hausdorff space is paracompact if and only...23 KB (3,481 words) - 18:27, 16 June 2024
- sets of X have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space. These conditions are examples of separation axioms and...12 KB (1,597 words) - 13:53, 8 April 2024
Hausdorff and Gromov–Hausdorff distance define metrics on the set of compact subsets of a metric space and the set of compact metric spaces, respectively. Suppose...80 KB (11,075 words) - 22:00, 22 August 2024- completely regular space that is also a Hausdorff space; there exist completely regular spaces that are not Tychonoff (i.e. not Hausdorff). Paul Urysohn had...13 KB (1,895 words) - 19:25, 20 May 2024
- to every compact Hausdorff space K a collection of maps K→C satisfying certain natural conditionsPages displaying wikidata descriptions as a fallback...28 KB (4,038 words) - 15:47, 19 June 2024
- but in a more subtle topological sense. In particular, every continuous function on a separable space whose image is a subset of a Hausdorff space is determined...14 KB (2,071 words) - 12:06, 2 March 2024
- {\displaystyle V} In particular, a compact Hausdorff space is uniformizable. In fact, for a compact Hausdorff space X {\displaystyle X} the set of all...26 KB (4,338 words) - 04:35, 18 July 2024
- {C} } ) be continuous. Functions with compact support on a topological space X {\displaystyle X} are those whose closed support is a compact subset of...17 KB (2,662 words) - 12:59, 18 August 2024
- set theory and general topology by Felix Hausdorff, Abraham Fraenkel and several others—to mention but a few examples. In many rapidly expanding fields
- be topological spaces, S ⊆ X {\displaystyle S\subseteq X} a compact subset and f : X → Y {\displaystyle f:X\to Y} a continuous function. Then f ( S ) {\displaystyle