TOPOLOGICAL STUDY OF GENERALIZED METRIC SPACES
The class of generalized metric spaces is introduced. A fixed point theorem in this class is proved and some applications to probabilistic metric spaces are given. Some topological properties generalized metric spaces are studied. We show that every generalized metric space is, naturally, a uniform space and moreover it is metrizable if the range set has countable cofinality. We also prove Baire’s theorem, uniform limit theorem and second countability result for generalized metric spaces.
generalized metric space, Baire’s theorem.