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1999/2000 On Relations Among Various Classes of I-a.e. Continuous Darboux Functions
Aneta Tomaszewska
Real Anal. Exchange 25(2): 695-702 (1999/2000).


This paper is devoted to relationships among various classes of $\cal I$-a.e. continuous functions (i.e., of functions whose sets of discontinuity points belong to certain $\sigma$-ideals $\cal I$ consisting of boundary sets). For instance, if $\cal K$ is the $\sigma$-ideal of first category sets and $\cal I$ denotes the $\sigma$-ideal of all sets that are: of Lebesque measure zero, $\sigma$-porous, or countable, then the set of $\cal I$-a.e. continuous functions is uniformly porous in the space of all $\cal K$-a.e. continuous Darboux functions from ${\mathbb R}^2$ into ${\mathbb R}^2$ equipped with the metric of uniform convergence. As a tool in the proofs, symmetric Cantor sets in ${\mathbb R}^2$ are used.


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Aneta Tomaszewska. "On Relations Among Various Classes of I-a.e. Continuous Darboux Functions." Real Anal. Exchange 25 (2) 695 - 702, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 3 January 2009

zbMATH: 1009.26012
MathSciNet: MR1778523

Primary: 26A15

Keywords: $\cal I$-a.e. continuous functions , $\sigma$-ideals , Cantor-like sets , Darboux functions , uniformly porous sets

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 2 • 1999/2000
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