Families of Darboux functions and topology having (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="script">J</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup></mml:math>)-property

Ivanova, Gertruda; Karasińska, Aleksandra; Wagner-Bojakowska, Elżbieta

doi:10.1016/j.topol.2019.03.021

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Cited by 3 publications

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“…There are many results discussing the comparison of porosity for different subsets of the function spaces (see [7][8][9][10]). It is interesting to consider not only continuous functions with respect to a given topology but also continuous with respect to the families which do not form a topology (see [5,11,12]).…”

Section: Introductionmentioning

confidence: 99%

On Strong Porosity of Some Families of Functions

Hejduk,

Ivanova,

Wiertelak

2023

Tatra Mountains Mathematical Publications

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Section: Introductionmentioning

confidence: 99%

On Strong Porosity of Some Families of Functions

Hejduk,

Ivanova,

Wiertelak

2023

Tatra Mountains Mathematical Publications

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The Smallest and the Largest Families of Some Classes of 𝒜-Continuous Functions

Ivanova

Karasińska

2023

Mathematica Slovaca

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In this paper, the families of functions continuous with respect to some family of subsets of the real line as a domain are considered. There is proved, among others, that if the family of subsets has some special property, then each function continuous with respect to this family is quasi-continuous (Corollary 2.2.1). We say that two families of subsets of the real line are equivalent if the families of functions which are continuous in generalized sense with respect to these families are equal. Limited considerations to the families which are generalized topologies with additional properties, we find in equivalence classes the smallest and the largest family with respect to inclusion (see Theorem 3.5).

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On lower density operators

Ivanova,

Wagner-Bojakowska

2024

Mathematica Slovaca

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The classical density topology is an extension of the natural topology on the real line, as the interior of arbitrary Lebesgue measurable set A is contained in the set of density points of A. Also each density point of A belongs to the closure of A for arbitrary measurable set A. In this paper, we concentrate on lower density operators for which the inclusions mentioned above are not fulfilled. In the first part, examples of such lower density operators generated by measure-preserving bijections are given. There are introduced three conditions to investigate lower density operators for which only the second inclusion holds. In the second part, the concept of operator D introduced by K. Kuratowski is applied to the characterization of such operators.

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Families of Darboux functions and topology having (J⁎)-property

Cited by 3 publications

References 18 publications

On Strong Porosity of Some Families of Functions

On Strong Porosity of Some Families of Functions

The Smallest and the Largest Families of Some Classes of 𝒜-Continuous Functions

On lower density operators

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