拓扑空间中的理想收敛

Ideal Convergence in Topological Space

用理想收敛结构解决定向拓扑的刻画问题,给出理想S极限和理想广义S极限可拓扑化的充要条件.结果表明:T0拓扑空间上的定向拓扑、理想S极限拓扑和理想广义S极限拓扑相同;定向空间中的理想S收敛是拓扑的当且仅当其为c-空间;定向空间中理想广义S收敛是拓扑的当且仅当其为局部强紧空间.

We used an ideal convergence structure to solve the characterization problem of directed topology,and provided necessary and sufficient conditions for the topological transformation of ideal S limits and ideal generalized S limits.The results show that the directed topology,the ideal S limit topology and the ideal generalized S limit topology are the same in T 0 topological spaces.The ideal S convergence in a directed space is topological if and only if it is a c-space.The ideal generalized S convergence in a directed space is topological if and only if it is a locally strongly compact space.