On density topologies with respect to invariant σ-ideals

• Autorzy: Hejduk J.
• Języki publikacji: EN

Abstrakty

EN

The density topologies with respect to measure and category are motivation to consider the density topologies with respect to invariant σ-ideals on R. The properties of such topologies, including the separation axioms, are studied.

Słowa kluczowe

EN

density point; density topology; separation axioms; invariant ideals and algebras

PL

punkt gęstości; topologia gęstości; aksjomaty oddzielania; niezmienne ideały i algebry

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2002
• Tom: Vol. 8, nr 2
• Strony: 201--219
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Hejduk J.

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

Bibliografia

• [1] Balcerzak, M., Hejduk, J., Density topologies for products of o-ideals, Real Anal. Exchange 20(1) (1994-95), 163-178.
• [2] Balcerzak, M., Hejduk, J., Wilczyriski, W., Wroriski, S., Why only measure and category?, Scient. Bull. Lodz Technical University Ser. Matematyka 695(26) (1994), 89-94.
• [3] Ciesielski, K., Larson, L., Ostaszewski, K., X-density continuous functions, Mem. Amer. Math. Soc. 515 (1994).
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• [5] Goffman, C., Waterman, D., Approximately continuous transformations, Proc. Amer. Math. Soc. 12 (1961), 116-121.
• [6] Hejduk, J., On the density topology with resect to an extension of Lebesgue measure, Real Anal. Exchange 21(2) (1995-96), 811-816.
• [7] Hejduk, J., Some properties of the density topology with respect to an extension of the Lebesgue measure, Math. Pannon. 9(2) (1998), 173-180.
• [8] Hejduk, J., Kharazishvili, A. B., On density points with respect to von Neumann’s topology, Real Anal. Exchange 21(1) (1995-96), 278-291.
• [9] Kuczma, M., An Introduction to the Theory of Functional Equations and Inequalities, PWN, Warszawa-Katowice, 1985.
• [10] Lukes, J., Malÿ, J., Zajicek, L., Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Math. 1189, Springer Verlag, Berlin, 1986.
• [11] Marczewski, E., Sur l’extension de la mesure lebesguienne, Fund. Math. 25 (1935), 551-558.
• [12] Oxtoby, J. C., Measure and Category, Springer Verlag, New York, 1980.
• [13] Poreda, W., Wagner-Bojakowska, E., Wilczyriski, W., A category analogue of the density topology, Fund. Math. 125 (1985), 167-173.
• [14] Wagner-Bojakowska, E., Sequences of measurable functions, Fund. Math. 112 (1981), 89-102.
• [15] Wilczyriski, W. A category analogue of the density topology, approximate continuity and the approximate derivative, Real Anal. Exchange 10(2) (1984-85), 241-265.
• [16] Wilczyriski, W., A generalization of density topology, Real Anal. Exchange 8(1) (1982-83), 16-20.