Pointwise density topology

• Autorzy: Magdalena Górajska
• Języki publikacji: EN

Abstrakty

EN

The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density points of any Borel set is Lebesgue measurable.

Słowa kluczowe

EN

Density point; Density topology; Pointwise convergence

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

wydano

2015-01-01

otrzymano

2013-01-02

zaakceptowano

2014-07-08

online

2014-10-28

Twórcy

autor

Magdalena Górajska

• Centre of Mathematics and Physics, Lodz University of Technology, Politechniki 22, 90-924 Lodz, Poland,

Bibliografia

• [1] Goffman C., Neugebauer C. J., Nishura T., The density topology and approximate continuity, Duke Math. J., 1961, 28, 497-506.
• [2] Górajska M., Wilczy´ nski W., Density topology generated by the convergence everywhere except on a finite set, Demonstratio Math. 2013, 45(1),197-208 .
• [3] Hejduk J., On density topologies with respect to invariant σ-ideals, J. Appl. Anal., 2002, 8(2), 201-219.
• [4] Kuczma M., An introduction to the theory of functional equation and inequalities, 2en ed., Birkhäuser Verlag AG, Basel-Boston- Berlin, 2009.
• [5] Nowik A., Vitali set can be homeomorphic to its complement, Acta Math. Hungar., 2007, 115(1-2), 145-154.[WoS]
• [6] Oxtoby J. C., Measure and category, Springer Verlag, New York-Heidelberg-Berlin, 1980.
• [7] Poreda W., Wagner-Bojakowska E., Wilczy´ nski W., A category analogue of the density topology, Fund.Math. 1985, 125, 167-173.
• [8] Wilczy´ nski W., Aversa V., Simple density topology, Rend. Circ. Mat. Palermo (2), 2004, 53, 344-352.
• [9] Wilczy´ nski W., Density topologies, Scientific Bulletyn Of Chełm Section of Mathematics And Computer Science, 2007, 1, 223-227.

Identyfikatory

DOI

10.1515/math-2015-0008