On the concept of generalization of I-density points

• Autorzy: Hejduk Jacek , Wiertelak Renata

Identyfikatory

DOI

10.7494/OpMath.2023.43.6.803

• Języki publikacji: EN

Abstrakty

EN

This paper deals with essential generalization of I-density points and I-density topology. In particular, there is an example showing that this generalization of I-density point yields the stronger concept of density point than the notion of I(J )-density. Some properties of topologies generated by operators related to this essential generalization of density points are provided.

Słowa kluczowe

EN

density topology; generalization of density topology

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 6
• Strony: 803--811
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Hejduk Jacek

• University of Łódź, Faculty of Mathematics and Computer Science, Banacha 22, PL-90-238 Łódź, Poland

• https://orcid.org/0000-0001-8222-0469

autor

Wiertelak Renata

• University of Łódź, Faculty of Mathematics and Computer Science, Banacha 22, PL-90-238 Łódź, Poland

• https://orcid.org/0000-0002-6423-504X

Bibliografia

• [1] M. Balcerzak, J. Hejduk, A. Wachowicz, Baire category lower density operators with Borel values, Results Math. 78 (2023), Article no. 2.
• [2] K. Ciesielski, L. Larson, K. Ostaszewski, I-density continous functions, Mem. Amer. Math. Soc. 107 (1994), no. 515.
• [3] J. Hejduk, G. Horbaczewska, On I-density topologies with respect to a fixed sequence, Reports on Real Analysis, Conference at Rowy (2003), 78–85.
• [4] J. Hejduk, R. Wiertelak, On the Abstract Density Topologies Generated by Lower and Almost Lower Density Operators, Traditional and Present-Day Topics in Real Analysis, Łodź University Press, 2013.
• [5] W. Poreda, E. Wagner-Bojakowska, W. Wilczyński, A category analogue of the density topology, Fund. Math. 125 (1985), 167–173.
• [6] R. Wiertelak, A generalization of density topology with respect to category, Real Anal. Exchange 32 (2006/2007), no. 1, 273–286.
• [7] R. Wiertelak, About I(J)-approximately continuous functions, Period. Math. Hungar. 63 (2011), no. 1, 71–79.
• [8] W. Wilczyński, A generalization of density topology, Real Anal. Exchange 8 (1982/1983), no. 1, 16–20.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)