拓扑空间的乘积

General Topology and its Applications Pub Date : 1978-04-01 DOI:10.1016/0016-660X(78)90001-6

J.E. Vaughan

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引用次数: 20

摘要

本文的主要目的是统一拓扑学中的一些定理，这些定理的结论表明拓扑空间的乘积具有类紧性。三个这样的定理是(1)Tychonoff定理:紧空间的每个积是紧的;(2)C.T. Scarborough和A.H. Stone的定理:最多N1个顺序紧空间的每个积是可数紧的;(3)N. Noble定理:Lindelöf p空间的一个可数积是Lindelöf。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Products of topological spaces

The main purpose of this paper is to unify a number of theorems in topology whose conclusions state that a product of topological spaces has a compactness-like property.Three such theorems are (1) the Tychonoff theorem: Every product of compact spaces is compact, (2) the theorem of C.T. Scarborough and A.H. Stone: Every product of at most N₁ sequentially compact spaces is countably compact, and (3) the theorem of N. Noble: A countable product of Lindelöf P-spaces is Lindelöf.

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