Almost compactness and near compactness in fuzzy topological spaces (Q1100756)

The author discusses the concept of almost compactness in a fuzzy setting as introduced by Concilio and Gerla; Q characterization of almost compactness has been given in terms of fuzzy regular closed and fuzzy regular open sets. It has been shown that a fuzzy weakly continuous image of a compact space is almost compact and a fuzzy strongly continuous image of a fuzzy almost compact space is compact. Further, nearly compactness has been introduced in a fuzzy setting along with characterization. It has been shown that the almost continuous and almost open image of a nearly compact space is nearly compact.