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Open Mathematics

formerly Central European Journal of Mathematics

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

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Volume 13, Issue 1


Volume 13 (2015)

Pointwise density topology

Magdalena Górajska
Published Online: 2014-10-28 | DOI: https://doi.org/10.1515/math-2015-0008


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


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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, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0008.

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

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