Completely continuous functions and R-map in fuzzifying topological space

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies introduced by Ying. The concepts of fuzzifying regular derived set, fuzzifying regular interior and fuzzifying regular convergence are studied and some results on above concepts are obtained. Also, the concepts of fuzzifying completely continuous functions and fuzzifying R-map are introduced and some important characterizations are obtained. Furthermore, some compositions of fuzzifying continuity with fuzzifying completely continuous functions and fuzzifying R-map are presented.