2019•Unpublished venueRequires access

ON CERTAIN GENERALIZATIONS OF METRIC SPACES

Huda Al-Malki

Abstract

A brief discussion of some basic concepts and notions in topology is included, Some properties of topological spaces and metric spaces are given. Some features of complete and compact spaces are also highlighted. The notion of a b-metric space with examples is given and various topological properties of the concept are presented. Strong b-metric spaces are discussed in details. Stone-type theorem and Tietze's type extension theorems are obtained in strong b-metric spaces. Fixed point theory in metric and b-metric spaces is given. Examples to support our results are also provided.

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Key concepts: Mathematics, Metric space, Convex metric space, Injective metric space, Uniform continuity, Topological space, Metric map, Pure mathematics