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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 28, 2014

Pointwise density topology

  • Magdalena Górajska EMAIL logo
From the journal Open Mathematics


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.


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Received: 2013-1-2
Accepted: 2014-7-8
Published Online: 2014-10-28
Published in Print: 2015-1-1

© 2015 Magdalena Górajska

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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