Duszyński, Zbigniew On pointwise \(\mathscr M\)-continuity of mappings. (English) Zbl 1313.54033 Tatra Mt. Math. Publ. 52, 1-8 (2012). The main result of the paper under review is the following Theorem. Let \((X,m_{X})\), \((Y,m_{Y})\) be supratopological spaces with \((Y,m_{Y})\) being \(m_{X}\)-2nd countable, and let \(f\: (X,m_{X})\to (Y,m_{Y})\) be an \(\mathscr M\)-semi-continuous mapping. Then the set \(D_{f}\) of all \(\mathscr M\)-discontinuity points of \(f\) is of \(m_{X}\)-first category. This generalizes a result of N. Levine [Am. Math. Mon. 70, 36–41 (1963; Zbl 0113.16304)]. Reviewer: Valeriu Popa (Chişinău) MSC: 54C08 Weak and generalized continuity Keywords:\(\mathscr M\)-space; supratopological space; pointwise \(\mathscr M\)-continuity; \(\mathscr M\)-semi-continuity Citations:Zbl 0113.16304 PDFBibTeX XMLCite \textit{Z. Duszyński}, Tatra Mt. Math. Publ. 52, 1--8 (2012; Zbl 1313.54033) Full Text: DOI References: [1] HUSAIN, \?.: Topology and Maps, Plenum Press, New York, 1977. · Zbl 0401.54001 [2] LEVINE, N.: Semi-open sets and, semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41. · Zbl 0113.16304 · doi:10.2307/2312781 [3] MAKI, H.: On generalizing semi-open sets and, preopen sets, in: Report for Meeting on Topological Spaces Theory and its Applications, 24-25 August 1996, Yatsushiro College Tech., pp. 13-18. [4] \?AKI. H.-CHANDRASEKHARA RAO, K.-NAGOOR GANI, \?.: On generalizing semi-open sets and, preopen sets, Pure Appl. Math. Sci. 49 (1999), 17-29. [5] NEUBRUNN, \?.: Quasi-continuity (topical survey), Real Anal. Exchange 14 (1988/89), 259-306. [6] POPA, V.-NOIRI, \?.: On M-continuous functions, Anal. Univ. ’Dunarea de Jos’ Galati, Ser. Mat. Fiz. Mec. Teor., Fasc. II 18(23) (2000), 31-41. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.