The Study Of Property In Some Generalized Paracompact Space

In this paper, it is mainly used strong semi-open set and then extendthe subparacompact space, metacompact space and submetacompact space,got three new topological space, named α-subparacompact space,α—metacompact space and α-submetacompact space, after it studied theproperties of these three spaces, and discussed the relationship among them.The main works are as follows:(1) This paper is mainly used strong semi-open set and then extend theconcept of subparacompact space, got α-subparacompact spaces, andgiven four equivalent characterizations of the α-subparacompact space,and discussed its some properties of the mapping.(2) This paper is mainly used strong semi-open set and then extend theconcept of metacompact space, got α—metacompact space, and then studiedthe properties of the α-metacompact space, including the property of itssubspace, characterizations and some properties under the mapping.(3) In1993, Yankui Song presented the concept of α-paracompactspace. In2007, Piyu Li gave an concept of the α-expandable space. Thispaper established the equivalence between the α-paracompact space andα-expandable space based on the α—metacompact space as a bridge.(4) This paper is mainly used strong semi-open set and then extend theconcept of submetacompact space, got α—submetacompact space, and thengave the equivalent characterizations of α-submetacompact space,discussed its connection with the α-subparacompact space and someproperties of the mapping.