Vietoris拓扑空间的道路连通性

Some Path Connect Properties On Vietoris Topological Space

研究Vietoris拓扑空间中的道路连通性与拓扑空间X中道路连通的关系,最终证明:(1)X为局部道路连通空间,ζ为(ρ0(X),Γy)中道路连通子集,C∈ζ,C为道路连通集,则A=∪ C C∈ζ为道路连通的。(2)(X,Γ)为道路连通的,那么(ζ,Γy)为道路连通的。(3)X为局部道路连通空间,(ζ1,Γy)为道路连通的,那么X为道路连通空间。

In this paper, we discuss some relation of path connect properties between Vietoris topological space and its basic topological space. Especially, it is proved that （1） If is local path connect space and is a path connect subset of ,and each member of is path connect ,then is path connect. （2）If is path connect space ,then is path connect. （3） If is local path connect space and is path connect space ,then is path connect spac.