The Study Of Expandable Spaces And Paracompact Spaces

In this thesis,α-expandable spaces and strong semi-paracompact spaces in general topological spaces, expandable spaces, strong semi-paracompact spaces and countably near STP-compactness in L-topological spaces are investigated. The primary studies are the following:(1) The concepts ofα-expandable spaces andω0-α-expandable spaces were given by Piyu Li in 2007. On the basis of this, the equivalent conditions ofα-expandable spaces andω0-α-expandable spaces are studied in the further way in this thesis. And some properties ofα-expandable spaces are inwestigated.(2) The concept of semi-paracompact spaces is generalized to strong semi-paracompact spaces by strong semi-open set in this thesis, and the equivalent conditions and the relative properties are discussed.(3) The concept of expandable spaces is given by r-strong locally finite in L-topological spaces in this thesis, and this property is L-good generalization property.(4) The concept of strong semi-paracompact spaces in general topological spaces is generalized toⅠ-strong semi-paracompact spaces andⅡ-strong semi-paracompact spaces in L-topological spaces.Ⅰ-strong semi-paracompactness is good generalization property andⅡ-strong semi-paracompactness is L-good generalization property.(5) On the basis of countable STP-compact sets in L-topological spaces, the concepts of countably near STP-compact sets and near STP-Lindelof property are given in this thesis, and the properties of them are studied.