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



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


	Fixed Point Theory, Volume 23, No. 1, 2022, 385-390, February 1st, 2022 DOI: 10.24193/fpt-ro.2022.1.24 Authors: Sumit Som, Lakshmi Kanta Dey and Wutiphol Sintunavarat Abstract: This paper deals with an open problem posed by Jleli and Samet in [1, M. Jleli and B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl, 20(3) 2018]. In [1, Remark 5.1], 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. Additionally, keeping in mind the fact that totally boundedness is not a topological property, in the setting of 𝓕-metric spaces are equivalent to that of usual metric spaces. Key Words and Phrases: 𝓕-metric space, metrizability, Cantor's intersection theorem. 2010 Mathematics Subject Classification: 54A20, 54E35, 54E50, 47H10. Published on-line: February 1st, 2022. Abstract pdf Fulltext pdf Back to volume's table of contents