Relative remote neighborhood family and the characterizations of ultra-fuzzy compactness

Abstract In this paper, the concept of relative remote neighborhood family in L-fuzzy topological spaces is introduced, by which some characterizations of ultra-fuzzy compactness are obtained. Using this concept, we have proved Alexander Subbase Lemma and TNXOHOB Product Theorem about ultra-fuzzy compactness. Furthermore, the ultra-fuzzy paracompactness defined by strong locally finite relative remote neighborhood family is proved to be an L-good extension.