| In this paper,S_c(X)space is extended to S(X)space,that is,a set family composed of the union of a finite convergence sequence and its convergence points,which is given to the hyperspace formed by Vietoris topology.This paper mainly studies some generalized metric properties of space.This dissertation mainly does the following three parts:In Chapter 2,We characterize the convergence of sequences in space S(X),and discuss some cardinal invariants in space,such as,the character,the pseudocharacter,the sn-character,snw-weight and so on.In Chapter 3,This paper mainly discusses the sequential connectedness and path connectedness between topological space X and hyperspace S(X).In Chapter 4,We mainly discuss some generalized metric properties in S(X),such as c-semi-stratifiable space,γ-space,c-semi-stratifiable space,etc.,and discuss whether the conclusion of the theorem“space X is a c-semi-stratifiable space if and only if F(X)is a c-semi-stratifiable space”can be extended to hyperspace S(X)(in fact,we give a partial answer to this question and apply the obtained conclusion to simplify the proving process of this theorem). |
