R_0-代数上的滤子拓扑空间

Filter topological spaces on R_0-algebras

在R0-代数M上以全体MP滤子之集为拓扑基建立了一个滤子拓扑空间(M,TM),给出了导集、闭包以及内部的计算公式。证明了(M,TM)是连通的、覆盖紧的且满足第一可数性公理;(M,TM)满足第二可数性公理当且仅当主滤子之集是可数集,(M,TM)不是T1的,不是T2的,也不是正则的或正规的;(M,TM)是T0空间当且仅当M是Boole代数。最后讨论了积R0-代数上的积空间。

A topological space（M,TM） with the set of all MP-filters as its basis on an R0-algebra M is introduced.Characterizations of differentiate,closure and interior operators in（M,TM） are obtained.It is proved that（M,TM） is connected and covering-compact and satisfies the first separation axiom,and it satisfies the second separation axiom if and only if the set of all principle filters is countable.However,（M,TM） is neither T1 nor regular.It is also proved that（M,TM） is T0 if and only if the R0-algebra M reduces to a Boolean algebra.Finally,product spaces on product R0-algebras are investigated.