关于相对仿紧空间的一些性质

摘要

The space of 2-Relative paracompact,1-Relative countably paracompact and Relative nearly paracompact are discussed.The results obtained are as follows：If the topological space is relative paracompact subspaces,then the topological space is relative nearly paracompact space;If subsets of a topological space is regular in the topological space,then the subset as the canonical subspace in topology space;If the paracompact subspaces of Topological space is regular,then the paracompact subspaces is canonical subspace;If the paracompact subspaces of topological space is T2,then the paracompact subspaces is canonical subspace,is regular subspace,and also is completely regular subspace.The subsets of a topological space is paracompact if and only if this subset is a topological space open cover in a subset of locally finite open refinement;A topological space is relatively open and closed subspace,If the topological space is 2-relative paracompact,then the topological space is relative paracompact subset.A both open and closed subsets of topological space is 2-paracompact,then this both open and closed subsets is ① the canonical subspace of the topological space,T3 subspace;② the canonical subspace of the topological space,subspace;③ the completely regular subspace of topological space,T31 2subspace.%对相对2-仿紧,相对可数1-仿紧,相对几乎仿紧等空间进行了讨论,得出如下结果：拓扑空间为相对仿紧子空间,则这个拓扑空间为相对几乎仿紧的;拓扑空间的子集在拓扑空间中正则,则该子集为拓扑空间的正则子空间;拓扑空间的仿紧子空间是正则的,则该仿紧子空间是正则子空间;拓扑空间的仿紧子空间是的,则仿紧子空间是正则子空间,是正规的,也是完全正则的;拓扑空间的子集是仿紧的当且仅当这个子集由拓扑空间中开集构成的开覆盖构成的任一开覆盖都有子集的开覆盖是拓扑空间中开覆盖的在子集中的局部有限开加细;一个拓扑空间是相对的开闭子空间,如果这个拓扑空间是相对2-仿紧的,则这个拓扑空间是相对仿紧子集;拓扑空间的一个既开又闭子集在该拓扑空间中是2-仿紧的,则这个既开又闭子集是①拓扑空间的正则子空间,子空间②拓扑空间的正则子空间,子空间③拓扑空间的完全正则子空间,子空间.