GERM 发表于 2025-3-21 19:07:25

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Bombast 发表于 2025-3-21 23:52:07

Compact Extensions,sets of . are open in . ∪{ξ}. Let us assume that . ≠ Ø. The compact space . ∪ {ξ} containing . as a dense open subspace has one essential deficiency. It does not even satisfy the . separation axiom since none of the sets {.}, where . ∈ ., is closed in . ∪ {ξ}.

triptans 发表于 2025-3-22 04:16:50

Book 1996tness appeared in mathematics for the first time as one of the main topo­ logical properties of an interval, a square, a sphere and any closed, bounded subset of a finite dimensional Euclidean space. Once it was realized that pre­ cisely this property was responsible for a series of fundamental fact

喊叫 发表于 2025-3-22 06:46:48

Compactness and Products,strictions on the cardinality of the family of factors and their separation properties, while other properties of compactness type can be destroyed already by the operation of the product of two spaces or even by the operation of topological squaring.

Cubicle 发表于 2025-3-22 10:20:41

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佛刊 发表于 2025-3-22 16:17:51

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佛刊 发表于 2025-3-22 18:51:29

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的阐明 发表于 2025-3-22 21:22:42

Lubica Benuskova,Nikola KasabovA space . is called . if every open cover of . contains a finite subcover. A compact Hausdorff space will be called a .. We shall see that the Hausdorff separation axiom has a great impact on the properties of compact spaces.

埋葬 发表于 2025-3-23 01:40:05

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Coma704 发表于 2025-3-23 05:49:40

Computational Nuclear Physics 2A . is a function defined on the class of all topological spaces or on any of its subclasses whose values are infinite cardinal numbers and has the property that for homeomorphic spaces the function assumes the same value. In general topology the theme of cardinal invariants plays a crucial role. We will provide some reasons why this is the case.
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查看完整版本: Titlebook: General Topology II; Compactness, Homolog A. V. Arhangel’skii Book 1996 Springer-Verlag Berlin Heidelberg 1996 Algebraic structure.Boolean