On a Generalization of Quasi-metric Space

2023/08/18 by Adhya, Sugata, Ray, A. Deb
#54A05 #54C08 #54E15 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2308.09580

Abstract

We find an extension of the quasi-metric (to be called g-quasi metric) such that the induced generalized topology may fail to form a topology. We show that g-quasi metrizability is a g-topologically invariant property of generalized topological spaces. Extending metric product and uniform continuity for g-quasi metric spaces, we note that a g-quasi metric may fail to be uniformly continuous in the extended sense unlike usual metric. Finally, we extend the study of completeness, Lebesgue property and weak G-completeness for g-quasi metric spaces.

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