Endograph Metric and a Version of the Arzelà–Ascoli Theorem for Fuzzy Sets

Juan J. Font, Sergio Macario and Manuel Sanchis ()
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Juan J. Font: Institut de Matemàtiques i Applicacions de Castelló (IMAC), Universitat Jaume I de Castelló, Av. Vicent Sos Baynat s/n, 12071 Castelló de la Plana, Spain
Sergio Macario: Institut de Matemàtiques i Applicacions de Castelló (IMAC), Universitat Jaume I de Castelló, Av. Vicent Sos Baynat s/n, 12071 Castelló de la Plana, Spain
Manuel Sanchis: Institut de Matemàtiques i Applicacions de Castelló (IMAC), Universitat Jaume I de Castelló, Av. Vicent Sos Baynat s/n, 12071 Castelló de la Plana, Spain

Mathematics, 2023, vol. 11, issue 2, 1-8

Abstract: In this paper, we provide several Arzelà–Ascoli-type results on the space of all continuous functions from a Tychonoff space X into the fuzzy sets of R n , ( F U S C B ( R n ) , H e n d ) , which are upper semi-continuous and have bounded support endowed with the endograph metric. Namely, we obtain positive results when X is considered to be a k r -space and C ( X , ( F U S C B ( R n ) , H e n d ) ) is endowed with the compact open topology, as well as when we assume that X is pseudocompact and C ( X , ( F U S C B ( R n ) , H e n d ) ) is equipped with the uniform topology.

Keywords: Arzelà–Ascoli theorem; compactness; fuzzy sets; endograph metric (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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