On fuzzy function spaces
type: Item
instance of: scholarly article
title: On fuzzy function spaces
zbMATH Open document ID: 0962.54004
DOI: 10.1155/S0161171299227275
author: G. Jäger
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2001-06-13T00:00:00Z
full work available at URL: https://eudml.org/doc/48752
review text: Given two fuzzy convergence spaces (in particular, two (Chang) fuzzy topological spaces) \((A,\lim^A)\) and \((B,\lim^B)\) and a fuzzy subset \(M\) of the function space \(A^B\), a convergence structure lim on \(M\) is called conjoining (resp. splitting) if \(\text{c-} \lim\leq \lim\) (resp. \(\text{c-} \lim \geq\lim)\) holds on \(M\), where c-lim is the ``standard'' convergence structure on the function space, see e.g. [\textit{E. Lowen}, \textit{R. Lowen} and \textit{P. Wuyts}, Fuzzy Sets Syst. 40, No. 2, 347-373 (1991; Zbl 0728.54001)]. The author gives some examples of splitting and conjoining convergence structures and applies such structures to the study of function spaces, in particular, to discuss the exponential law in the category FCS of fuzzy convergence spaces (which is known to be Cartesian closed). As a special case, the compact open fuzzy topology on a function space (defined in a way, similar to \textit{Y. Peng}'s [Topological structure of a fuzzy function space -- the pointwise convergent topology and compact open topology, Kexue Tongbao, Foreign Lang. Ed. 29, 289-292 (1984)]) is considered.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54A20
zbMATH DE Number: 1417971
zbMATH Keywords: fuzzy convergence structure
zbMATH Keywords: fuzzy function space
zbMATH Keywords: compact open fuzzy topology
reviewed by: Alexander Šostak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1417971