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On some subclasses of the family of Darboux Baire 1 functions

Ivanova G., Wagner-Bojakowska E.

Opuscula Mathematica

2014

Vol. 34, no. 4

777--788

We introduce a subclass of the family of Darboux Baire 1 functions f : R → R modifying the Darboux property analogously as it was done by Z. Grande in [On a subclass of the family of Darboux functions, Colloq. Math. 17 (2009), 95–104], and replacing approximate continuity with I-approximate continuity, i.e. continuity with respect to the I-density topology. We prove that the family of all Darboux quasi-continuous functions from the first Baire class is a strongly porous set in the space DB1 of Darboux Baire 1 functions, equipped with the supremum metric.

Microscopic and strongly microscopic sets on the plane. Fubini theorem and Fubini property

Karasińska A., Wagner-Bojakowska E.

Demonstratio Mathematica

2014

Vol. 47, nr 3

581--594

In this paper, we introduce the notions of microscopic and strongly microscopic sets on the plane and obtain a result analogous to Fubini Theorem.

Resolvability of I - density topology

Wagner-Bojakowska E.

Zeszyty Naukowe Wyższej Szkoły Informatyki

2001

Vol. 1, Nr 1

35-37

Some modifications of density topologies

Horbaczewska G., Wagner-Bojakowska E.

Journal of Applied Analysis

2001

Vol. 7, nr 1

91-105

In this paper we introduce two topologies on the plane connected with the notions of density and I-density. Their definitions are based on the notion of a regular density point. We investigate connections between them and the density and I-density topologies on the plane and on the real line. We consider axioms of separation and functions continuous with respect to these topologies.