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点是G_(δ~-)集的∑~*-空间的构成定理(英文)
The Decomposition Theorem for Σ*-spaces With Gδ-Points

彭良雪
PENG Liang-xue

北京工业大学应用数理学院 北京, 100022
(College of Applied Science, Beijing University of Technology, Beijing, 100022, P. R. China

收稿日期: 2004-02-25
出版日期: 2004-02-25

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摘要 在林寿与我最近合作的一篇文章中指出了∑*-空间的构成定理需重新考虑.本文就是要证明在空间X的每个点是Gδ-集的条件下该构成定理是成立的,所得的结论是: X是T1且每个点是Gδ-集的∑*-空间,如果f:X→Y是闭的满连续映射,则在Y中有一σ-闭离散子空间Z,使得对每个y∈Y\Z,f-1(y)是X的ω1-紧子空间.为得到该主要结果,本文证明了若空间X是每个点是Gδ-集的次亚紧空间.则X中的每个闭离散子集是X中的Gδ-集.
关键词 ∑*-空间强∑*-空间次亚紧空间ω1-紧σ-离散    
Abstract:Lin and I pointed out that the decomposition theorem for Σ*-spaces should be considered again recently. In this paper I show that the decomposition theorem is true if every point of the space X is also a Gδ-set of X. The main conclusion is: If space X is a T1, Σ*-space with every point of X is a Gδ-set, and f : X→Y is a closed onto map, then there is a σ-closed discrete subspace Z of Y, such that f-1(y) is an wwww-compact subspace of X for every y ∈ Y \ Z. In getting the main conclusion I show that every closed discrete subset of a space X is a Gδ-set of X, if X is a submetacompact space and every point of X is a Gδ-set of X.
Key words strong Σ *-space    submetacompact space    ω1-compact    δ-discrete
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