Cantor's intersection theorem in the setting of $\mathcal{F}$-metric spaces

Sumit Som; Lakshmi Kanta Dey

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arXiv · 1903.10001

Cantor's intersection theorem in the setting of $\mathcal{F}$-metric spaces

Sumit Som·Lakshmi Kanta Dey

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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 $\mathcal{F}$-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 $\mathcal{F}$-metric spaces are equivalent to that of usual metric spaces.

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BibTeX RIS

Sumit Som, Lakshmi Kanta Dey. 2019-03-24. Cantor's intersection theorem in the setting of $\mathcal{F}$-metric spaces. https://arxiv.org/abs/1903.10001

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