The concept of fuzzifying topologies appeared in 1980 under the name L-fuzzy topology, where L is a completely distributive complete lattice. It must be pointed out that Hoehle, Lowen, Sostak and Gerla were aware of the possibility to establish fuzzifying topology and in particular, Sostak and his students have done some interesting work in this field. In 1991-1993, Ying introduced the fuzzifying topology and elementally developed fuzzy topology from a new direction with semantic method of continuous valued logic.