σ_1-空间及弱nested T_2算子

本文研究了具有弱nested T2算子的空间的遗传性、有限乘积性并讨论了与正则空间、第一可数空间、同胚映射之间的关系.

A NOTE ON THE IMAGES OF M_1-SPACES

In this note,we give some conditions concerning that the countably bi-quotient closed mappings, and the closed mappings with each fiber having a σ-closure preserving outer base, preserve M1-spaces.

A SUBCLASS OF M1 -SPACES

In this paper,We defined M1^#-space,in some meaning,it is a dual concept of M1^#-space. We proved that Metrizable→M1^#→M1.

ON STRONGLY M_1-SPACES

In this paper we have obtained the fallowing results: (1)A space X is strongly M1 if and only if X is a paracompact σ-space and every closed subset F of X has a σ-FCP open outer base. (2)If X is strongly M1 and F is closed in X, then the quotient space X/F is strongly M1. (3) The following propositions are equivalent; (Ⅰ) Every closed image of any strongly M1-space is srongly M1. (Ⅱ) In every closed image of any strongly M1-space, each point has a (σ)-FCP open neibourhood (briefly, nbd)base.

一类单调正规空间

以邻域约定为工具讨论了一类特殊的单调正规空间 ,证明了具有垫状对基的拓扑空间是M1 空间 ,部分地回答了Ceder在 196

关于《M_1-空间的和定理》一文的注记

《数学研究与评论》1988年第一期研究通讯栏目上刊登了论文《M_1-空间的和定理》。我们这篇简短的注记在于说明: (1)上述论文所引进的“强遗传闭包保持集族”的概念等价于“遗传闭包保持集族”的概念。 (2)上述论文中的定理3的结论是不正确的。 关于(1)若正则拓扑空间X的子集族B是X的遗传闭包保持集族,那么由B的元的闭包所组成的集族亦是X的遗传闭包保持集族。