Density topology generated by the convergence everywhere except for a finite set

• Autorzy: Górajska, M. , Wilczyński, W.
• Języki publikacji: EN

Abstrakty

EN

In this paper we shall study a density-type topology generated by the convergence everywhere except for a finite set similarly as the classical density topology is generated by the convergence in measure. Among others it is shown that the set of finite density points of a measurable set need not be measurable.

Słowa kluczowe

PL

punkt gęstości; topologia gęstości

EN

density point; density topology

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 1
• Strony: 197--208
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Górajska, M.

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

autor

Wilczyński, W.

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

Bibliografia

• [1] C. Goffman, C. J. Neugebauer, T. Nishura, Density topology and approximate continuity, Duke Math. J. 28 (1961), 497–506.
• [2] J. Hejduk, Density topologies with respect to invariant σ-ideals, University of Łódź, (1997).
• [3] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, PWN, (1985).
• [4] J. C. Oxtoby, Measure and Category, Springer Verlag, New York-Heidelberg-Berlin, (1980).
• [5] W. Poreda, E. Wagner-Bojakowska, W. Wilczyński, A category analogue of the density topology, Fund. Math. 125 (1985), 167–173.
• [6] W. Wilczyński, V. Aversa, Simple density topology, Rend. Circ. Mat. Palermo (2) 53 (2004), 344–352.
• [7] W. Wilczyński, Density topologies, Scientific Bulletin of Chełm, Section of Mathematics and Computer Science 1 (2007), 223–227.
• [8] W. Wilczyński, W. Wojdowski, Complete density topology, Indag. Math. (N.S.) 18(2) (2007), 295–303.