<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We introduce some families of functions ƒ : ℝ → ℝ modifying the Darboux property analogously as it was done by [Maliszewski, A.: On the limits of strong Świątkowski functions, Zeszyty Nauk. Politech. Łódź. Mat. 27 (1995), 87-93], replacing continuity with A-continuity, i.e., the continuity with respect to some family A of subsets in the domain. We prove that if A has (*)-property then the family DA of functions having A-Darboux property is contained and dense in the family DQ of Darboux quasi-continuous functions. </p></abstract>

We introduce some families of functions ƒ : ℝ → ℝ modifying the Darboux property analogously as it was done by [Maliszewski, A.: On the limits of strong Świątkowski functions, Zeszyty Nauk. Politech. Łódź. Mat. 27 (1995), 87-93], replacing continuity with A-continuity, i.e., the continuity with respect to some family A of subsets in the domain. We prove that if A has (*)-property then the family DA of functions having A-Darboux property is contained and dense in the family DQ of Darboux quasi-continuous functions.

On some Modification of Świtąkowski Property

University of Łódź Faculty of Mathematics and Computer Science ul. Banacha 22 PL–90-238 Łódź POLAND

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On some Modification of Świtąkowski Property"}

We introduce some families of functions ƒ : ℝ → ℝ modifying the Darboux property analogously as it was done by [Maliszewski, A.: On the limits of strong...

On some Modification of Świtąkowski Property

Published Online: Aug 15, 2014

Page range: 101 - 109

Received: Dec 02, 2013

DOI: https://doi.org/10.2478/tmmp-2014-0009

Keywords
Darboux property, strong Świątkowski property, quasi-continuity

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On some Modification of Świtąkowski Property

Published Online: Aug 15, 2014

Page range: 101 - 109

Received: Dec 02, 2013

DOI: https://doi.org/10.2478/tmmp-2014-0009

KeywordsDarboux property, strong Świątkowski property, quasi-continuity

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Darboux property, strong Świątkowski property, quasi-continuity