点集拓扑中各种紧致空间之间的相互蕴含关系

Relationships Among Compact Spaces in Point Set Topology

介绍了紧致空间、可数紧致空间、列紧致空间、序列紧致空间、局部紧致空间、仿紧致空间的基本概念,讨论了上述几种紧致空间之间的相互蕴涵关系。对于紧致空间之间具有的蕴含关系,先给出了相应的结论,然后从理论上进行了详细的验证;对于紧致空间之间不具有的蕴含关系,给出了具体的反例。

In this paper,many concepts were introduced such as compact space,countable compact space,sequentially compact space,sequences of the tight space,local compact space and paracompact space,and the relationship among these spaces was discussed. The conclusion was put forward and demonstrated theoretically in detail,and concrete counterexamples were given.