仿sober与超sober拓扑空间

On pseudo-sober topological spaces and ultra-sober topological spaces

对拓扑空间的sober分离性细致分析后引入类似于sober性的另外两种分离性:仿sober和超sober分离性;讨论了诸分离性的相关性质和相互关系,证明了非T1的仿sober空间一定是连通的、可分的sober空间;还探讨了dom a in上Scott拓扑与仿sober、超sober分离性的关系,证明了仿(超)sober偏序集均为代数dom a in.

Soberity is a separation property of topological spaces. In this paper, two concepts of soberlike separations： pseudo-sober separation and ultra-sober separation are introduced and investigated. Some properties and relations of them are drawn. It is proved that a non-T1 pseudo-sober topological space must be sober, separable and connected. The relationships of domains in the Scott topology and pseudo-（uhra-） sober spaces are also explored. It is proved that a pseudo-（uhra-） sober poser is an algebraic domain.