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Titlebook: General Topology II; Compactness, Homolog A. V. Arhangel’skii Book 1996 Springer-Verlag Berlin Heidelberg 1996 Algebraic structure.Boolean

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樓主
發(fā)表于 2025-3-21 19:07:25 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱General Topology II
副標(biāo)題Compactness, Homolog
編輯A. V. Arhangel’skii
視頻videohttp://file.papertrans.cn/383/382144/382144.mp4
叢書名稱Encyclopaedia of Mathematical Sciences
圖書封面Titlebook: General Topology II; Compactness, Homolog A. V. Arhangel’skii Book 1996 Springer-Verlag Berlin Heidelberg 1996 Algebraic structure.Boolean
描述Compactness is related to a number of fundamental concepts of mathemat- ics. Particularly important are compact Hausdorff spaces or compacta. Com- pactness 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 facts related to those sets such as boundedness and uniform continuity of continuous func- tions defined on them, compactness was given an abstract definition in the language of general topology reaching far beyond the class of metric spaces. This immensely extended the realm of application of this concept (including in particular, function spaces of quite general nature). The fact, that general topology provided an adequate language for a description of the concept of compactness and secured a natural medium for its harmonious development is a major credit to this area of mathematics. The final formulation of a general definition of compactness and the creation of the foundations of the theory of compact topological spaces are due to P.S. Alek
出版日期Book 1996
關(guān)鍵詞Algebraic structure; Boolean algebra; Compact space; Kohomologie; Separation axiom; cardinal invariant; co
版次1
doihttps://doi.org/10.1007/978-3-642-77030-2
isbn_softcover978-3-642-77032-6
isbn_ebook978-3-642-77030-2Series ISSN 0938-0396
issn_series 0938-0396
copyrightSpringer-Verlag Berlin Heidelberg 1996
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 23:52:07 | 只看該作者
Compact Extensions,sets of . are open in . ∪{ξ}. Let us assume that . ≠ ?. 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}.
板凳
發(fā)表于 2025-3-22 04:16:50 | 只看該作者
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
地板
發(fā)表于 2025-3-22 06:46:48 | 只看該作者
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.
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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.
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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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