Density, ψ-density and continuity-Reference-Cited by-同舟云学术

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Density, ψ-density and continuity

Published:2017-11-01 Issue:6 Volume:67 Page:1525-1534
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Filipczak Małgorzata¹,Terepeta Małgorzata²,Wilczyński Władysław¹

Affiliation:

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

2. Center of Mathematics and Physics Łódź University of Technology al . Politechniki 11 90-924 Łódź Poland

Abstract

Abstract In this paper we consider classes of continuous functions with three kinds of topologies on the domain and/or range of the function: the natural topology, density topology and ψ-density topology. We focus on functions from the classes 𝓒 ψd and 𝓒 dψ .

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0067/pdf

Reference15 articles.

1. Ciesielski, K.—Larson, L.: Various continuities with the density, I-density and ordinary topology on R, Real Anal. Exchange 17 (1991-92), 183–210.

2. Ciesielski, K.—Larson, L.—Ostaszewski, K.: I-density continuous functions, Mem. Amer. Math. Soc. 107 (1994).

3. Denjoy, A.: Sur les fonctions sérivées sommables, Bull. Soc. Math. France 43 (1915), 161–248.

4. Filipczak, M.: σ-ideals, topologies and multiplication, Bull. Soc. Sci. Lódź, Vol. LII, (2002), 11–16.

5. Filipczak, M.: Families of ψ-approximate continuous functions, Tatra Mt. Math. Publ. 28 (2004), 219–225.

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