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The Metrization Problem in [0, 1]-Topology Peng
Version 1
: Received: 5 September 2023 / Approved: 6 September 2023 / Online: 6 September 2023 (10:28:03 CEST)
A peer-reviewed article of this Preprint also exists.
Chen, P. The Metrization Problem in [0,1]-Topology. Mathematics 2023, 11, 4430. Chen, P. The Metrization Problem in [0,1]-Topology. Mathematics 2023, 11, 4430.
Abstract
The paper discusses the classification of fuzzy metrics based on their continuity conditions, dividing them into Erceg, Deng, Yang-Shi, and Chen metrics. It explores the relationships between these types of fuzzy metrics, concluding that a Deng metric in [0,1]-topology must also be Erceg, Chen, and Yang-Shi metrics. The paper also proves that the product of countably many Deng pseudo-metric spaces remains a Deng pseudo-metric space, and demonstrates some σ-locally finite properties of Deng metric space. Additionally, the paper constructs two interrelated mappings based on normal space and concludes that if a [0,1]-topological space is T1 and regular, and its topology has a σ-locally finite base, then it is Deng metrizable, and thus Erceg, Yang-Shi, and Chen metrizable as well.
Keywords
fuzzy point; [0, 1]-topology; Deng pseudo-metric; s-locally finite base; regular; T1-space; distance; metrizable
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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