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On some modification of Świątkowski property

In: Tatra Mountains Mathematical Publications, vol. 58, no. 1
Gertruda Ivanova - Elżbieta Wagner-Bojakowska
Detaily:
Rok, strany: 2014, 101 - 109
Kľúčové slová:
Darboux property, strong Świątkowski property, quasi-continuity.
O článku:
We introduce some families of functions $f\!:\mathbb{R}\rightarrow\mathbb{R}$ modifying the Darboux property analogously as it was done by [Maliszewski, A.: \textit{On the limits of strong \'{S}wi\c{a}tkowski functions}, Zeszyty Nauk. Politech. \L\'od\'z. Mat. \textbf{27} (1995), 87--93], replacing continuity with $\mathcal{A}$-continuity, i.e., the continuity with respect to~some family $\mathcal{A}$ of subsets in the domain. We prove that if $\mathcal{A}$ has (*)-property then the family $\mathcal{D}_\mathcal{A}$ of functions having $\mathcal{A}$-Darboux property is contained and dense in the family $\mathcal{DQ}$ of Darboux quasi-continuous functions.
Ako citovať:
ISO 690:
Ivanova, G., Wagner-Bojakowska, E. 2014. On some modification of Świątkowski property. In Tatra Mountains Mathematical Publications, vol. 58, no.1, pp. 101-109. 1210-3195.

APA:
Ivanova, G., Wagner-Bojakowska, E. (2014). On some modification of Świątkowski property. Tatra Mountains Mathematical Publications, 58(1), 101-109. 1210-3195.