Neighborhoods, bases and continuity in fuzzy topological spaces

Abstract

It is shown that fuzzy continuous functions can be characterized by the closure of fuzzy sets, a subbasis for a fuzzy topology and fuzzy neighborhoods. Additional results are obtained conceming the collection of all fuzzy topologies on a fixed set, the interior of a fuzzy set, the closure of a fuzzy set, a fuzzy limit point, the derived fuzzy set and the relative fuzzy topology. © 1978 Rocky Mountain Mathematics Consortium.