Comparison of some families of real functions in porosity terms

Author:

Filipczak Małgorzata1,Ivanova Gertruda2,Wódka Julia3

Affiliation:

1. Faculty of Mathematics and Computer Sciences Łódź University ul . Stefana Banacha 22 90-238 Łódź Poland

2. Institute of Mathematics Pomeranian University in Słupsk Kozietulskiego 6–7 76-200 Słupsk Poland

3. Institute of Mathematics Łódź Technical University ul . Wólczańska 215 93–005 Łódź Poland

Abstract

Abstract We consider the following families of real-valued functions: Darboux, quasi-continuous, Świątkowski functions and strong Świątkowski functions. The aim of this paper is to compare this sets in terms of topology.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference16 articles.

1. Bruckner, A. M.—Ceder, J. C.: Darboux continuity, Jahresber. Deutsch. Math. Ver. 67 (1965), 93–117.

2. Dolzenko, E. P.: Boundary properties of arbitrary functions, Izvestija Akad Nauk SSSR, Ser. mat. 31 (1967)(in Russian), 3–14.

3. Grande, Z.: On a subclass of the family of Darboux functions, Colloq. Math. 117 (2009), 95–104.10.4064/cm117-1-6

4. Ivanova, G.—Wagner-Bojakowska, E.: On some modification of Darboux property, Math. Slovaca 66 (2016), 79–89.

5. Kempisty, S.: Sur les fonctions quasicontinues, Fund. Math. 19 (1932), 184–197.10.4064/fm-19-1-184-197

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