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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

1 Issue per year


IMPACT FACTOR 2015: 0.512

SCImago Journal Rank (SJR) 2015: 0.521
Source Normalized Impact per Paper (SNIP) 2015: 1.233
Impact per Publication (IPP) 2015: 0.546

Mathematical Citation Quotient (MCQ) 2015: 0.39

Open Access
Online
ISSN
2391-5455
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Volume 13, Issue 1 (Jan 2015)

Issues

Pointwise density topology

Magdalena Górajska
  • Centre of Mathematics and Physics, Lodz University of Technology, Politechniki 22, 90-924 Lodz, Poland
  • Email:
Published Online: 2014-10-28 | DOI: https://doi.org/10.1515/math-2015-0008

Abstract

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.

Keywords : Density point; Density topology; Pointwise convergence

References

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  • [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 .

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  • [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. [Web of Science]

  • [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.

About the article

Received: 2013-01-02

Accepted: 2014-07-08

Published Online: 2014-10-28

Published in Print: 2015-01-01


Citation Information: Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0008. Export Citation

© 2015 Magdalena Górajska. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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