超空间的连通性和c半层空间性质

The Properties of Sequential Connectedness and C-semi-stratifiable Spaces in Hyperspaces

设X是Hausdorff拓扑空间,超空间S(X)中的每一元素是X中有限个收敛序列的并且赋予Vietoris拓扑.主要讨论当空间X分别是序列连通、道路连通和c半层空间,则超空间S(X)是否分别是序列连通、道路连通和c半层空间.对这些问题给出(部分)回答.

Let X be a Hausdorff topological space.The symbol S(X)denotes the hyperspace of finite unions of convergent sequences in the space X,which is endowed with the Vietoris topology.In this paper,we mainly discuss if X is a sequentially connected space,path connected space and c-semi-stratifiable space respectively,then is S(X)is sequential connectedness,path connectedness and c-semi-stratifiable respectively.We give some(partial)answers to these questions.