点是Gδ-集的∑*-空间的构成定理

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w1-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.

The Decomposition Theorem for ∑*-spaces With Gδ-Points

Lin and I pointed out that the decomposition theorem for ∑*-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 Ti,∑*-space with every point of X is a Gδ-set, and f: X → Y is a closed outo map, then there is a σ-closed discrete subspace Z of Y, such that f-1(y) is an w1-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 G δ-set of X.