有限补空间和可数补空间的一些性质

Some Properties of Finite Complement Space and Countable Complementary Space

在有限补拓扑空间和可数补拓扑空间的基本性质的基础上对他们子集的导集、闭集、内部和边界进行讨论,求出了有限补拓扑空间的子集在有限和无限的情况下的导集、闭集、内部和边界,及可数补拓扑空间的子集在可数和不可数的情况下的导集、闭集、内部和边界。通过它们性质的研究使我们对这两个空间有更清楚的认识。

This paper discusses some basic properties of finite complement spaces and countable complementary spaces in general topology. Derived set, closed set, interior and boundary under the conditions with finite and infinite as well as countable and uncountable are obtained. And through studying the properties, we can clearly understand these two spaces.