In: Tatra Mountains Mathematical Publications, vol. 52, no. 2
Zbigniew Duszyński
Detaily:
Rok, strany: 2012, 1 - 8
Kľúčové slová:
$\mathpzc{M}$-space, supratopological space, pointwise $\mathpzc{M}$-continuity, $\mathpzc{M}$-semi-continuity
O článku:
Classical Levine's theorem [N. Levine: \textit{Semi-open sets and semi-continuity in topological spaces}, Amer. Math. Monthly {\bf70} (1963), 36–41] asserts that for a semi-continuous mapping on a second countable topological space, the discontinuity points form a 1st category set. There are two directions in literature in which this result is generalized: by considering either multi-valued mappings or mappings on some second noncountable spaces (for the latter, see for instance [T.Neubrunn: \textit{Quasi-continuity (topical survey)}, Real Anal. Exchange {\bf14} (1988/89), 259–306]). In this paper, we offer another path, namely, the path of so-called $\mathpzc{M}$-spaces, essentially weaker than the topological ones. Pointwise \mbox{$\mathpzc{M}$-continuity} of a mapping between two $\mathpzc{M}$-spaces is defined and characterized. These characterizations are the basic tool for our generalization.
Ako citovať:
ISO 690:
Duszyński, Z. 2012. On pointwise $\mathpzc{M}$-continuity of mappings. In Tatra Mountains Mathematical Publications, vol. 52, no.2, pp. 1-8. 1210-3195.
APA:
Duszyński, Z. (2012). On pointwise $\mathpzc{M}$-continuity of mappings. Tatra Mountains Mathematical Publications, 52(2), 1-8. 1210-3195.