Relative compact fuzzy subsets in fuzzy convergence spaces

Abstract

Besides compactness the weaker notion of relative compactness plays an important role in topology. This paper generalizes a definition of relative compactness given by Chadwick [1] for fuzzy topological spaces to fuzzy convergence spaces as studied by the author ([4–6,8]). We prove that it is a “good extension”, develop the necessary theory and finally give two applications to the theory of the fuzzy Richardson compactification and to the theory of fuzzy function spaces.