完全正则空间的一个刻画

A Depiction on Completely Regular Space

给出了集合X上的弱一致结构的定义 ,通过弱一致结构给出了刻画完全正则空间的一个等介刻画 ,即拓扑空间 (X ,T)是完全正则空间的充分必要条件为X上存在一个弱一致结构 ,其中T是该弱一致结构所诱导的拓扑 .

This paper gives a definition of weak uniformity on set X, and an equival condition of completely regular spaces, that is, a topological space (X,T) is a completely regular space if and only if there exists a weak uniformity on X, and T() is the topology induced by the weak uniformity.