不分明拓扑由唯一拟近性结构所生成的条件

THE CONDITIONS OF A L-FUZZY TOPOLOGY INDUCED UNIQUELY BY A L-FUZZY QUASI-PROXIMITY

本文讨论了不分明拓扑有唯一拟近性结构所生成的条件.证明:(i)L-fuzzy 拓扑空间(L^X,δ)可由L^X 上唯一拟近性结构(?)所生成的(?)是完全的;(ii)当r 是L^X 上完全近性结构时,则(?)L^X 上一致结构(?)(r)使得δ_r=δ(?) (r)且r^(?)=r(?)(r)=r.

In this paper,we discuss the conditions of a L-fuzzy topology induced uniquely by a L-fuzzy quasi-proximity,and prove that(i)the conditions of a L-fuzzy topological space(L^X,δ)induced uniquely by an L-fuzzy quasi-proximity r iff r is perfect;(ii)if ris a perfect L-fuzzy proximity,then there exists an L-fuzzy uniformity (?)(r)on L^X such that δ_r=δ(?)(r)and r(?)=r(?)(r)=r.