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On symmetrically porouscontinuous functions

  • Stanisław Kowalczyk and Małgorzata Turowska EMAIL logo
Published/Copyright: November 10, 2016

Abstract

In the present paper, we introduce the notion of symmetrically porouscontinuous functions. We investigate some properties of symmetric porouscontinuity and its connections with the notion of porouscontinuity, studied by Borsík and Holos in [2]. We prove that there are 2𝔠 symmetrically porouscontinuous functions, which extends results of [1] concerning ρ-upper continuous functions.

MSC 2010: 54C30; 26A15; 54C08

References

[1] Bienias M., Głąb S. and Wilczyński W., Cardinality of sets of ρ-upper and ρ-lower continuous functions, Bull. Soc. Sci. Lett. Łódź Ser. Rech. Deform. 64 (2014), 71–80. Search in Google Scholar

[2] Borsík J. and Holos J., Some properties of porouscontinuous functions, Math. Slovaca 64 (2014), no. 3, 741–750. 10.2478/s12175-014-0237-3Search in Google Scholar

[3] Bruckner A. M., O’Malley R. J. and Thomson B. S., Path derivatives: A unified view of certain generalized derivatives, Trans. Amer. Math. Soc. 283 (1984), 97–125. 10.1090/conm/042/807973Search in Google Scholar

[4] Dolženko E. P., Boundary properties of arbitrary functions (in Russian), Math. USSR Izv. 31 (1967), 3–14. 10.1070/IM1967v001n01ABEH000543Search in Google Scholar

[5] Zajíček L., Porosity and σ-porosity, Real Anal. Exchange 13 (1987/88), 314–350. 10.2307/44151885Search in Google Scholar

Received: 2016-1-23
Revised: 2016-9-5
Accepted: 2016-9-17
Published Online: 2016-11-10
Published in Print: 2016-12-1

© 2016 by De Gruyter

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