| 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. |
