几乎半预连续模糊多值映射

On fuzzy almost semi-precontinuous multifunctions

本文在作者 [2 ] 定义的模糊半预开集的基础上 ,在一般拓扑空间 ( X,T)与模糊拓扑空间 ( Y,T1)之间引入了模糊下与上几乎半预连续多值映射的概念 ,并借助于映射 F* 与 F* 证明了模糊下几乎半预连续多值映射的五个等价条件 :( 1 ) U∈ T1,F* ( U) SPint F* ( SPint SPcl U) ;( 2 )若 U是 Y中模糊正则半预开集则 F* ( U)是 X中的半预开集 ;( 3) U∈ T1,F* ( SPint SPcl U)是 X中的半预开集 ;( 4 )若 V是 Y中模糊闭集 ,F* ( V) SPcl F* ( SPcl SPint V) ;( 5 )若 V是 Y中的模糊正则半闭集 ,则 F* ( V)是 X中的半预闭集。

In this paper,based on the definition of fuzzy semi-preopen sets ,between a general topological space (X,T) and fuzzy topological space (Y,T 1) the concepts of fuzzy lower and upper almost semi precontinuous mulitifunctions are introduced,and using the mapping F * and F * five equivalent conditions of a fuzzy lower semi precontinuous multifunctions hare been proved:(1) U∈T 1,F*(U) Spint F *(SPintSPcl U );(2) F *( U ) is semipreopen set in X ,for every fuzzy regular semi preopen sets Uin Y;(3)U∈T 1,F *(SPintSPcl U ) is semipreopen set in X;(4) F *(V) SPclF *(SPclSPintV),for every fuzzy closd sets V in Y ;(5) F *(V) is semipreslosd set in X ,for every fuzzy regular semi preclosd sets V in Y.Fuzzy upper semi precontinuous multifunction also have analogical results.