<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Classical Levine's theorem [N. Levine: <italic>Semi-open sets and semi-continuity in topological spaces</italic>, Amer. Math. Monthly <bold>70 </bold>(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: <italic>Quasi-continuity</italic><italic>(topical survey)</italic>, Real Anal. Exchange <bold>14</bold> (1988/89), 259-306]). In this paper, we offer another path, namely, the path of so-called M-spaces, essentially weaker than the topological ones. Pointwise M -continuity of a mapping between two M-spaces is defined and characterized. These characterizations are the basic tool for our generalization.</p></abstract>

Classical Levine's theorem [N. Levine: Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (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: Quasi-continuity(topical survey), Real Anal. Exchange 14 (1988/89), 259-306]). In this paper, we offer another path, namely, the path of so-called M-spaces, essentially weaker than the topological ones. Pointwise M -continuity of a mapping between two M-spaces is defined and characterized. These characterizations are the basic tool for our generalization.

On pointwise ℳ-continuity of mappings

Casimirus the Great University Institute of Mathematics pl. Weyssenhoffa 11 PL-85-072 Bydgoszcz, POLAND

Tatra Mountains Mathematical Publications

{"article-title":"On pointwise ℳ-continuity of mappings"}

Classical Levine's theorem [N. Levine: Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41] asserts that for a...

On pointwise ℳ-continuity of mappings

Published Online: Nov 19, 2012

Page range: 1 - 8

DOI: https://doi.org/10.2478/v10127-012-0020-1

Keywords
ℳ-space, supratopological space, pointwise ℳ-continuity, ℳ-semi-continuity.

This content is open access.

On pointwise ℳ-continuity of mappings

Published Online: Nov 19, 2012

Page range: 1 - 8

DOI: https://doi.org/10.2478/v10127-012-0020-1

Keywordsℳ-space, supratopological space, pointwise ℳ-continuity, ℳ-semi-continuity.

This content is open access.

Keywords
ℳ-space, supratopological space, pointwise ℳ-continuity, ℳ-semi-continuity.