Compactness in the endograph uniformity

Iván Sánchez

https://orcid.org/0000-0002-4356-9147

Mexico

Universidad Autónoma Metropolitana image/svg+xml

Departamento de Matemáticas

Submitted: 2023-03-18

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Accepted: 2023-07-30

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Published: 2024-04-02

DOI: https://doi.org/10.4995/agt.2024.19400

Copyright (c) 2023 Applied General Topology

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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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Keywords:

Fuzzy sets, Endograph uniformity, Endograph metric, Sendograph uniformity, Sendograph metric, Completeness, Compactness

Supporting agencies:

This research was not funded

Abstract:

Given a uniform space (X,U), we denote by F*(X) to the family of fuzzy sets u in (X,U) such that u is normal and upper semicontinuous. Let UE be the endograph uniformity on F*(X). In this paper, we mainly characterize totally bounded and compact substes in the uniform space (F*(X),UE).

 

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