Endograph Metric and a Version of the Arzelà–Ascoli Theorem for Fuzzy Sets
Juan J. Font,
Sergio Macario,
Manuel Sanchis
Affiliations
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
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 Rn, (FUSCB(Rn),Hend), 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 kr-space and C(X,(FUSCB(Rn),Hend)) is endowed with the compact open topology, as well as when we assume that X is pseudocompact and C(X,(FUSCB(Rn),Hend)) is equipped with the uniform topology.
