L-fuzzy拓扑空间中的强聚点和强导集

The Strong Accumulation Point and the Strong Derived Set in L-fuzzy Topological Spaces

本文提出了L-fuzzy拓扑空间的强聚点和强导集概念,这是既不同于[5]文的聚点也不同于[6]文的N-聚点的一种新的聚点定义,结果表明它具有一般拓扑学中相应的几乎全部结论。例如,A^-=A∨A^d,杨忠道定理成立,x_γ为L—fuzzy集A中的强聚点当且仅当A-x_1中有收敛于x_γ的分子网,以及当(L^x,δ)为ST_(-1)空间时,(A∨B)~d=A^d∨B^d,等等。

In this paper, the concepts of the strong accumulation point and the derived set in L-fuzzy topological spaces are introduced and their properties are systematically discussed. The results show that their properties are nearly paralleled with those results in general topology. For examper, A_-=A∨A^d, C.T. Yang's theorem, the x_λ is the strong accumulation point in L-fuzzy set A if and only if there's a molecular net coverged to x_λ in A-x_1, and if (L^x, δ) is a ST_(-1)-space then (A∨B)~d=A^d∨B^d. etc.