拓扑中分离公理的统一处理

在1]中,我们从泛拓扑概念出发,提出了拓扑中分离公理的一个一般模式,并给出了相应的非标准条件。本文完全采用经典观点对分离公理作出一个新的统一处理,建立了若干命题用以指明分离性质具有遗传性、可积性、商保持性以及拓扑空间到某个幂空间的可嵌入性的一般性条件;得到了联系分离性质与复盖性质的几个一般结果;指明了邻域分离性与函数分离性在本文的观点之下完全得到统一。

A Unified Treatment of Separation Axioms in Topology

Various separation axioms with d ifi'erent separatedness are used in general topology. In This paper we give a general form of separation axioms and set up several theorems to unify various results about separation properties of topological spaces, in particular, in the view of this paper, two sorts of separatedness, separation by neighborhoods and separation by functions, are unified.