集合套拓扑第二邻域的定义及性质

The Definition and Characters of the Second Neighbourhood of SEB Topology

本文在文献[3]的基础上,通过给出集合套拓扑空间中给出一种新的邻域—第二邻域的定义,并给出了它的一些性质,证明了由邻域系,基与子基可分别确定X上的一个唯一的集合套拓扑并且这种拓扑确定的邻域系与原来的邻域系一致。

In this paper,we provide a new neighbourhood definition of SEB topology.In the neighbourhood,we give the definations of base for SEB topology and subbase for it and we disscuss the characters of it and we prove the SEB topology on X which can be defined by the system of neighbourhood,base,subbase repectively is unique and the system of neighbourhood of this topology is uniform with the system of neighbourhood of the previous topology.