Abstract
In this paper, the concepts of α-ultra-closed filter and α-finite intersection property are introduced into L-fuzzy topological space. By using these two concepts, the Nice-compactness is characterized again. Then, we construct a fuzzy T 1-compactification of a T 1- L-fuzzy topological space, and the crisp Wallman-type compactification is extended to L-fuzzy topological space for the first time.
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