直观模糊特别拓扑空间中的半开集和半连续

journal6 ›› 2000, Vol. 21 ›› Issue (1): 69-72.

直观模糊特别拓扑空间中的半开集和半连续

(吉首大学数学与计算机科学系, 湖南吉首 416000)

出版日期:2000-03-15 发布日期:2013-01-16

Semi-open Sets and Semi-Continuity in Intuitionistic Fuzzy Special Topological Spaces

( Department of Mathematics and Computer Science, Jishou Univeristy, Jishou 416000, Hunan China)

Online:2000-03-15 Published:2013-01-16
About author:YANG Xin- mei, male, born in 1963 at the ci ty of Changsha. Lecturer at Jishou University, The main researching field:Geneval topology.

摘要/Abstract

摘要：将半开集和半连续的概念引入直观模糊特别拓扑空间, 得到它们的一些性质:一个直观模糊特别集是直观模糊特别半开集的充要条件是 A cl[ int(A) ] ; 直观模糊特别半开集族的任意并是直观模糊特别半开集; 直观模糊特别开集是直观模糊特别半开集; ( X, τ)的子空间( ( Y,φ)中的集合 A 是( X, τ)中的半开集,则它也是( Y, φ)中的半开集; 连续函数是半连续的,但逆不成立; 强半连续是半连续的, 但逆不成立;函数 f 是半连续的当且仅当对于f ( x ) O, O 是 Y中的直观模糊特别开集,存在 X 中的直观模糊特别半开集A 使x A 且f (A ) O; 函数 f 是强半连续的当且仅当 Y中的每一直观模糊特

关键词： 直观模糊特别集, 直观模糊特别半开集, 半连续, 强半连续

Abstract: The notions of semi-open sets and semi-continuity in intuitionistic were introduced, their some properties were obtained: an intuitionistic fuzzy special set is an intuitionistic fuzzy special semi-open set if and only i f A cl [ int ( A) ] , A_i : i∈I be an arbitrary family of IFSSOS's , then O is an I FSSOS, Let A Y ~ X ~and A is an IFSSOS in(X , σ) , then A is an IFSSOS in ( Y, φ); Continucty implies semi-continuity but not conversely, Strongly semi-continuity implies semi-continuity but not conversely,The function f : X Y is semi-continuous f and only if for f ( x ) O, O is an IFSSOS in Y there exis ts and IFSSOS A in X such that x ∈A and f ( A ) O,The function f : X→Y is strongly semi- continuous if and only if the preimage of each IFSSCS in Y IFSSCS in X .

Key words: intuitionistic fuzzy special set, intuitionistic fuzzy special semi-open sets, semi-continuous, strongly semicontinuous

杨新梅. 直观模糊特别拓扑空间中的半开集和半连续[J]. journal6, 2000, 21(1): 69-72.

YANG Xin-Mei. Semi-open Sets and Semi-Continuity in Intuitionistic Fuzzy Special Topological Spaces[J]. journal6, 2000, 21(1): 69-72.

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[2]	杨新梅. 直观模糊性特别拓扑空间中的S- 可数性及S- Lindelof空间[J]. journal6, 2000, 21(2): 71-73.