格值诱导空间与分明空间的关系

The Relation Between Induced Space on Lattces and Topological Space

本文主要研究格值诱导空间。证明了在这类空间中分子网的收敛、紧性、映射的连续(开或闭)性等价于诱导它的分明空间的相应性质。同时讨论了L—Fuzzy拓扑空间的导出空间。最后,推广了王国俊同志的《L—Fuzzy 拓扑空间中的连通性》中的一个定理。

In this paper,we discussed induced space.It is proved convergence ofa net,compactness.Continuty of a mapping has similar propertise asthat in“base space”e.g.if two general topological space homeomorphismthen induced space homeomorphism.General topological space is compactif induced space is nice-compact.Moreover,we discussed that the alikequestion between the L-Fuzzy topological space which dirived generaltopological space by that.Finally,it is improved a theorem in (2).