摘要
本文旨在解决与L—fuzzy拓扑空间的紧致性有关的如下三个问题:(1)建立超F紧的网刻划。(2)寻找Hausdorff良紧空间是超F紧的充要条件。(3)讨论L-fuzzy子集的良紧性和强F紧性在整体性质上的差异。
In this paper main results are as follows: 2.3. Theorem. Suppose(L^X,η) is an L-fuzzy topological space and S={S(n) is a molecular net. Then the followings are equivalent (1) (L^X,η) is fuzzy ultracompact. (2) (L^X,ω_L(τ_L(η)) is N-compact. (3) If m(S)≥a then the support net suppS of S has a limit point in (X,τ_L(η) (4) If m(S)≥ then S has a transitive limit point with valuea. (5) If M(S)≥a then there is a subnet T of S such that m(T)≥a,having a transitive limit point with valuea. (6) If M(S)≥a then suppor net suppS of S has a closure point with (?)aluea. 3.7. Theorem. Suppose (L^X,η) is a Hausdorff N-compact space,Then the follwing are equivalent. (1) (L^X,η) is fuzzy ultracompact. (2) (L^X,η_f) is weakly induced. (3) (L^X,η_f) is strong Hausdorff space. 4.4.Theorem, suppose A is a subset in (L^X,η). Then A is N-compact iff A is strong fuzzy compact and the nonempty intersecation of A and A and arbitrary closed set is M-arrival.
