摘要
一引言本文对文献[1]介绍的超紧性、良紧性、强F紧性及F紧性在弱诱导空间与(强)Hausdorff空间的等价性进行了系统的研究,得到了较为整齐的结果.在此基础上,构造了一个满层Hausdorff良紧而非强Hausdorff非超紧的反例,该反例结合已得结论,完满地回答了文[1]中提出的两个公开问题5.4.10和6.4.31。此外,本文还给出了Hausdorff良紧空间是超紧的若干条件.
In this paper, the equivalent of ultra-fuzzy compactness, N-compactness, strong fuzzy compactness and fuzzy compactness in weakly induced spaces and (strong) Hausdirff spaces are discussed. A counterexample was given in which we defined an L-fuzzy topological space which is fully stratified, Hausdorff and JV-compact but neither strong Hausdorff nor ultra-fuzzy compact, hence solves two open problems. Finally some conditions are given for a Hausdorff N-compact space to be an ultra-fuzzy compact space.
