特殊预拓扑空间的连通性与局部连通性

The Connectivity and Local Connectivity of Several Special Pre-topological Spaces

摘要

摘要:讨论了多于两点的离散拓朴空间、奇偶预拓扑空间、区间套预拓扑空间等特殊的预拓扑空间的连通性与局部连通性,建立了序预拓扑空间的概念,并证明字典序预拓扑空间是连通且局部连通的.

Abstract:The connectivity and local connectivity of several special pre-topological spaces, such as the discrete pre-topological space with more than two points, the parity pre-topological space and the interval sets pre-topological space, were put under examination. Then the notion of the ordered pre-topological space was established, and the lexicographical ordered pre-topological space was proved to be connected and, to be exact, locally connected.