一个外部运算定理及其条件的独立性

A THEOREM BY EXTERIOR OPERATOR AND INDEPENDENCE OF ITS CONDITIONS

本文对点集拓扑学中由外部算子确定拓扑的方法进行讨论.首先给出外部算子的定义,然后证明了外部算子确定拓扑的外部运算定理并且讨论了外部运算中条件的相互独立性,最后证明:与外部算子可交换的一一映射是同胚映射。

This paper is devoted to the study of the method of describing topology in point - set topology by exterior operator. First a new concept of exterior operator is defined, then the theorem of determining topological space by exterior operator and the independ- ence of boundary operator- conditions is established. Finally it is proved that one - one mapping which may exchange with the exterior operator is a homeomorphism.