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On some modification of Darboux property

  • Gertruda Ivanova EMAIL logo and Elżbieta Wagner-Bojakowska
Published/Copyright: April 29, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

We introduce some family of functions f: ℝ → ℝ modifying Darboux property analogously as it was done in GRANDE, Z.: On a subclass of the family of Darboux functions, Colloq. Math. 117 (2009), 95-104, and changing approximate continuity with 𝓘-approximate continuity, i.e. continuity with respect to the 𝓘-density topology. We prove that our family is a strongly porous set in the space of Darboux functions having the Baire property and that each function from our family is quasi-continuous.

Keywords: Darboux property; strong Świa̧tkowski property; Baire property; 𝓘-approximate continuity; quasicontinuous; functions; porous set
MSC: Primary 26A15; Secondary 54C08; 54C30; 54C35

  1. This paper has been communicated by Ján Borsík

References

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Received: 2013-2-27
Accepted: 2013-6-3
Published Online: 2016-4-29
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0117
Keywords for this article
Darboux property; strong Świa̧tkowski property; Baire property; 𝓘-approximate continuity; quasicontinuous; functions; porous set

Articles in the same Issue

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  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
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  9. Research Article
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  13. Research Article
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