模糊拓扑空间中的边界

On Boundaries in Fuzzy Topological Spaces

本文讨论模糊拓扑空间中模糊集合边界的新的重要性质。如果(?)={A_α:α∈Λ}是模糊拓扑空间(X,τ)中的模糊集合形成的局部有限族,可得出如下结果: (1)(?)中元素的边界所成之集合族仍然是局部有限的;(2)(?)中元素的边界之并是闭的;(3)(?)中元素的边界之并包含(?)中元素之并的边界;(4)b(E×F)(?)(b(E)×(?))∪b(?)×b(F)。

This paper deals with the new important properties about the fuzzy set boundary in fuzzy topological spaces, If (?)={A_α;α∈Λ} is a locally finite family of fuzzy subsets of a fuzzy topological space (X,τ). we shall prove the following: (1) The family of boundary of members of (?) is also locally finite, (2) The union of boundary of members of (?) is closed, (3) The union of boundary of members of (?) contains the boundary of the union of members of (?), (4) b(E×F)(?)(b(E)×(?))∪b(?)×b(F).