Pointwise density topology

Open Mathematics

Górajska Magdalena¹ 

[1] Centre of Mathematics and Physics, Lodz University of Technology, Politechniki 22, 90-924 Lodz, Poland;

关键词: Density point;    Density topology;    Pointwise convergence;   

DOI  :  10.1515/math-2015-0008

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown