The Number of Fuzzy Clopen Sets in Fuzzy Topological Spaces

Abstract

We show the number of fuzzy clopen sets in an arbitrary fuzzy topological space can be any natural number greater than 1 if it is finite. We give an upper bound for this number. We shall also prove that the number of all crisp fuzzy clopen sets in an arbitrary fuzzy topological space is a power of 2 if it is finite. Keywords: clopen, enumerating, finite set, fuzzy clopen*This research has taken place while the author has a sabbatical leave from Yarmouk University.