Ideal Banach category theorems and functions
Mathematica Bohemica, Tome 122 (1997) no. 1, pp. 13-20.

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Based on some earlier findings on Banach Category Theorem for some "nice" $\sigma$-ideals by J. Kaniewski, D. Rose and myself I introduce the $h$ operator ($h$ stands for "heavy points") to refine and generalize kernel constructions of A. H. Stone. Having obtained in this way a generalized Kuratowski's decomposition theorem I prove some characterizations of the domains of functions having "many" points of $h$-continuity. Results of this type lead, in the case of the $\sigma$-ideal of meager sets, to important statements of Abstract Analysis such as Blumberg or Namioka-type theorems.
DOI : 10.21136/MB.1997.126189
Classification : 54A25, 54B15, 54C08, 54E52
Mots-clés : Banach Category Theorem; categorical almost continuity; Blumberg space; separate and joint continuity 
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Piotrowski, Zbigniew. Ideal Banach category theorems and functions. Mathematica Bohemica, Tome 122 (1997) no. 1, pp. 13-20. doi : 10.21136/MB.1997.126189. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.1997.126189/

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