拓扑保持映射下的拓扑性质

Topological properties under topology-preserving mappings

讨论在拓扑保持映射定义下的拓扑性质,得到了在T0分离公理的假设下拓扑保持映射是同胚映射.此外,还讨论拓扑保持映射下几类基数不变量,并得到拓扑保持映射保持连通性、紧性、仿紧性、可数紧性等.

The topological properties under the definition of topologically preserving mappings are discussed.And it is obtained that topologically preserving mappings are homeomorphisms under the assumption of T0 separation axiom.Moreover,some cardinality invariants under topologically preserving mappings,are dicussed and it is obtained that the connectivity,compactness,paracompactness,countable compactness are preserved by topologically preserving mappings.