Fuzzy properties in fuzzy convergence spaces (Q1607909)

In most papers in fuzzy topology concrete topological properties are viewed in a crisp way, that is they either hold or fail. On the other hand there are some works where topological properties are ``fuzzified'' in the sense that they become fuzzy predicates, that is, they can hold to a certain degree between \(0\) and \(1\), see e.g. [\textit{R. Lowen}, Inf. Sci. 36, 17-27 (1985; Zbl 0588.03038)], see also the previous paper of the author [Fuzzy Sets Syst. 125, No. 2, 167-175 (2002; Zbl 0994.54008)]. Also the aim of this paper is to fuzzify several properties for (Chang) fuzzy topological spaces and for (Lowen) fuzzy convergence spaces. In particular, properties of closedness and compactness of a fuzzy set in a fuzzy convergence space and the continuity property of a mapping of fuzzy convergence spaces are fuzzified. The obtained theory generalizes the corresponding ``crisp'' theory in the realm of fuzzy topology and fuzzy convergence spaces. As the basic tools for his theory the author uses prefilters and residual implication.