Cantor's intersection theorem in the setting of F-metric spaces

2019/03/24 by Som, Sumit, Dey, Lakshmi Kanta
#47H10 #54A20 #54E50 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1903.10001

Abstract

This paper deals with an open problem posed by Jleli and Samet in \cite[ M.~Jleli and B.~Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl, 20(3) 2018]JS1. In \cite[ Remark 5.1]JS1 They asked whether the Cantor's intersection theorem can be extended to F-metric spaces or not. In this manuscript we give an affirmative answer to this open question. We also show that the notions of compactness, totally boundedness in the setting of F-metric spaces are equivalent to that of usual metric spaces.

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