Some modifications of density topologies

• Autorzy: Horbaczewska G. , Wagner-Bojakowska E.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

density topologies; comparison of topologies; regular density point

PL

topologie gęstości; porównanie topologii; regularny punkt gęstości

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2001
• Tom: Vol. 7, nr 1
• Strony: 91--105
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Horbaczewska G.

• Faculty of Mathematics, Łódź University, Stefana Banacha 22, 90-238 Łódź, Poland

autor

Wagner-Bojakowska E.

• Faculty of Mathematics, Łódź University, Stefana Banacha 22, 90-238 Łódź, Poland

Bibliografia

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• [3] Ciesielski, K., Larson, L., Ostaszewski, K., I-density continuous functions, Mem. Amer. Math. Soc. 107(515) (1994).
• [4] Goffman, C., Neugebauer, C., Nishiura, T., Density topology and approximate continuity, Duke Math. J. 28 (1961), 497-505.
• [5] O’Malley, R. J., Baire" 1 Darboux functions, Proc. Amer. Math. Soc. 60 (1976), 187-192.
• [6] Oxtoby, J. C., Measure and Category, Springer Verlag, New York, 1971.
• [7] Poreda, W., Wagner-Bojakowska, E., Wilczyński, W., A category analogue of the density topology, Fund. Math. 125 (1985), 167-173.
• [8] Poreda, W., Wagner-Bojakowska, E., Wilczyński, W., Remarks on I-density and I-approximately continuous functions, Comment. Math. Univ. Carolin. 26(3) (1985), 553-563.
• [9] Wilczyński, W., A generalization of density topology, Real Anal. Exchange 8(1) (1982-83), 16-20.