The Research On Several Problems Of Generalized Topology

The central question of topology is to establish and study topological invariants. Generalized topology as the promotion of topology possesses some nice topological characterizations. Meanwhile, it extends basic topological theory. The research method of replacing open sets with generalized open sets is usually employed to study generalized topology. In recent years, the above method is extensively applied in the field of generalized topology by some topologists, and they obtain some nice research findings.Sequentially open set is a kind of generalized open set. In this paper, we introduce sequentially expandable spaces and sequentially paracompactness and Seq - compactness by means of the method of replacing open sets with generalized open sets, and give some characterizations of them as well as the relations with them.This paper is parted into three chapters.In the first chapter, we introduce the background knowledge of related. In the second chapter, we introduce the concept of sequentially expandable spaces, and give some their characterizations, the main result obtained in the second chapter as follows.Theorem 2.4.3 If every sequentially open cover of X has a locally finite open refinement, then X is sequentially expandable.Theorem 2.4.4 Perfect mappings preserve sequential expandability.In the third chapter, we introduce the concept of sequentially paracompact spaces, give some their characterizations and show that the relationship between sequentially paracompactness and Seq - compactness. The main results obtained in the third chapter as follows, theorem 3.3.7, theorem 3.3.9, theorem 3.4.4.