On fuzzy function spaces (Q1970276)

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.