关于D-空间

ON D-SPACES

本文研究了用邻域对应定义的空间类.利用构造性的方法,证明了有限多个狭义拟仿紧空间的并是aD-空间及λ-半层空间是D-空间,得到了拓扑空间是aD-空间或D-空间的充分条件,一般化了已有的相应结果.

In this article, we research the class of spaces defined by a neighborhood assignment for a topological space. By a method of conformation, we show that, if a space X is the union of finitely many strong quasi-paracompact spaces, then X is an aD-space, and every λ-semistratifiable space is a D-space. We obtain the sufficient conditions of a topological space to be an aD-space or a D-space, and generalize several results obtained by Arhangel’skiǐ in [4] and [6].