Fuzzy almost continuity and its pointwise characterization by dual points and fuzzy nets (Q749906)

This paper presents the local properties of fuzzy almost continuity and fuzzy weak continuity in [\textit{C. L. Chang}, J. Math. Anal. Appl. 24, 182-190 (1968; Zbl 0167.510)]. In order to obtain the local properties, the authors introduce these notions at fuzzy-pointwise with a slight modification of the fuzzy points used by \textit{Pu Pao Ming} and \textit{Liu Ying Ming} [J. Math. Anal. Appl. 76, 571-599 (1980; Zbl 0447.54006)]. A characterization of fuzzy almost continuity at a fuzzy point is given by dual fuzzy points and fuzzy nets. Following this approach, the authors are able to provide localizable structures, thus generalizing results of \textit{M. K. Singal} and \textit{A. R. Singal} [Yokohama Math. J. 16, 63-73 (1968; Zbl 0191.208)].