On some subclasses of the family of Darboux Baire 1 functions | Zendy

Gertruda Ivanova | Zendy; Elżbieta Wagner-Bojakowska | Zendy

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On some subclasses of the family of Darboux Baire 1 functions

Author(s) -

Gertruda Ivanova,

Elżbieta Wagner-Bojakowska

Publication year - 2014

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2014.34.4.777

Subject(s) - baire category theorem , mathematics , baire space , baire measure , class (philosophy) , pure mathematics , complete metric space , infimum and supremum , darboux integral , discrete mathematics , metric space , artificial intelligence , computer science , geometry , curvature

We introduce a subclass of the family of Darboux Baire 1 functions \(f:\mathbb{R}\rightarrow\mathbb{R}\) modifying the Darboux property analogously as it was done by Z. Grande in [On a subclass of the family of Darboux functions, Colloq. Math. 17 (2009), 95-104], and replacing approximate continuity with \(\mathcal{I}\)-approximate continuity, i.e. continuity with respect to the \(\mathcal{I}\)-density topology. We prove that the family of all Darboux quasi-continuous functions from the first Baire class is a strongly porous set in the space \(\mathcal{DB}_1\) of Darboux Baire 1 functions, equipped with the supremum metric

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