Opuscula Mathematica
Opuscula Math. 34, no. 4 (), 777-788
Opuscula Mathematica

On some subclasses of the family of Darboux Baire 1 functions

Abstract. 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.
Keywords: Darboux property, strong Świątkowski property, Baire property, \(\mathcal{I}\)-approximate continuity, quasi-continuity.
Mathematics Subject Classification: 26A15, 54C08.
Cite this article as:
Gertruda Ivanova, Elżbieta Wagner-Bojakowska, On some subclasses of the family of Darboux Baire 1 functions, Opuscula Math. 34, no. 4 (2014), 777-788, http://dx.doi.org/10.7494/OpMath.2014.34.4.777
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.