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Around the Świątkowski-type conditions

Filipczak Małgorzata, Terepeta Małgorzata

Journal of Applied Analysis

2023

Vol. 29, nr 2

205--217

In this paper, we will focus on different types of Świątkowski conditions: Świątkowski, strong Świątkowski and weak Świątkowski conditions. We present the main properties of the families of functions fulfilling such conditions.

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.

On sets determined by sequences of quasi-continuous functions

Wesołowska J.

Journal of Applied Analysis

2001

Vol. 7, nr 2

271-283

The aim of the paper is to characterize those sets of points at which sequence of real functions from a given class F converges as well as sets of points of convergence to infinity of such sequences. As F we consider quasi-continuous functions and some other subclasses of Baire measurable functions.

On the products of bounded Darboux Baire one functions

Maliszewski A.

Journal of Applied Analysis

1999

Vol. 5, nr 2

171-185

It is shown that for each k > 1, if f is a Baire one function and f is the product of k bounded Darboux (quasi-continuous) functions, then f is the product of k bounded Darboux (quasi-continuous) Baire one functions as well.