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On pointwise \(\mathscr M\)-continuity of mappings. (English) Zbl 1313.54033

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)].

MSC:

54C08 Weak and generalized continuity

Citations:

Zbl 0113.16304
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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
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