Studies On The Properties Of Base-countably Weak Paracompact Spaces And Locally K-weak Paracompact Spaces

In this paper, we mainly introduced two classes of generalized paracompactspaces and focused on some related main cover properties about base-countably weakparacompact and locally k-weak paracompact spaces. The main results can be drawnas follows: the property of base-countably weak paracompact spaces, including theequivalent characterization of base-countably weak paracompact spaces, the inverseinvariant property under perfect mapping and base-countably weak paracompactmapping.Let X and Y are both base-countably weak paracompact spaces, then theproduct spaces X×Yis base-countably weak paracompact if Y is locally compact.There are similar to the above, three kinds of locally k-weak paracompact spaces aredefined, and there main properties are discussed respectively, including the heredityproperty for both open subspaces and closed subspaces, and the study of countableunion of locally k-weak paracompact spaces. It is easy to show that the image of onekind of locally k-weak paracompact spaces under an open-closed finite-to-one map isstill keeping, locally k-weak paracompact spaces are an inverse invariant ofclosed Lindelo&&fmapping. In addition, some classical product properties in three kindsof locally k-weak paracompact spaces are mainly obtained. Based on the relatedproperties of the above analysis and discussion, we further enrich and develop thetheories of the classes of generalized paracompact spaces.