Fuzzy topological space for real line generated by fuzzy metric space

Fuzzy numbers, fuzzy points are all made vaguely from real numbers. Hence t here is some sort of connection among them. The real numbers metric space a nd the level 1 fuzzy points metric space can form two equivalent metric spa ces. And the level 1 fuzzy points metric space is a subspace of fuzzy metri c space. Therefore, we may extend the real numbers metric space into the fu zzy metric space. And we could have induced a fuzzy topological space for R (= (-infinity, +infinity)) by using the concepts of family of neighborhoods in fuzzy metric space. Also, the level 1 fuzzy points topological space is equivalent to the real numbers topological space. That is the fuzzy topolo gical space for R is an extension of the real numbers topological space. An d we did get some interesting results. (C) 2000 Elsevier Science B.V. All r ights reserved.