Fuzzy topology on fuzzy sets: Product fuzzy topology and fuzzy topological groups (Q1964188)

Considering the notion of fuzzy topology on fuzzy sets [\textit{M. K. Chakraborty} and \textit{T. M. G. Ahsanullah}, ibid. 45, No. 1, 103-108 (1992; Zbl 0754.54004)] the present author introduces the concept of product fuzzy topology and investigates the product invariance of fuzzy Hausdorffness, compactness and connectedness. Using the notion of product fuzzy topology the author introduces the concept of fuzzy topological groups. In so doing, the author alters the notion of fuzzy topology taking all constant fuzzy sets into consideration -- an idea similar to \textit{R. Lowen} [J. Math. Anal. Appl. 56, 621-633 (1976; Zbl 0342.54003)].