柔拓扑空间的连通性

Connectedness of Soft Topological Spaces

研究了柔拓扑空间的连通性,在柔拓扑空间中定义了隔离柔集,利用隔离柔集给出了连通柔拓扑空间和连通柔集的概念,并为连通柔拓扑空间提供了等价的定义。通过引入了柔拓扑空间之间的连续序同态,证明了柔拓扑空间的连通性在连续序同态下具有不变性,最后得出了柔拓扑空间连通的几个充分条件。

Connectedness of soft topological space is studied. The concept of separated soft set is introduced in a soft topological space. Using separated soft set, the notions of connected soft topological space and connected soft set are defined, and equivalent definitions of connected soft topological space are given. By introducing the notion of continuous order-homomorphism between soft topological spaces,connectedness of a soft topological space is proved to be invariant under a continuous order-homomorphism. Finally, some sufficient conditions for a soft topological space to be connected are obtained.