Pointwise density topology
Open Mathematics (2015)
- Volume: 13, Issue: 1, page 75-82, electronic only
- ISSN: 2391-5455
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topMagdalena Górajska. "Pointwise density topology." Open Mathematics 13.1 (2015): 75-82, electronic only. <http://eudml.org/doc/268792>.
@article{MagdalenaGórajska2015,
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.},
author = {Magdalena Górajska},
journal = {Open Mathematics},
keywords = {Density point; Density topology; Pointwise convergence; -density point; pointwise convergence; pointwise density topology},
language = {eng},
number = {1},
pages = {75-82, electronic only},
title = {Pointwise density topology},
url = {http://eudml.org/doc/268792},
volume = {13},
year = {2015},
}
TY - JOUR
AU - Magdalena Górajska
TI - Pointwise density topology
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 75
EP - 82, electronic only
AB - 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.
LA - eng
KW - Density point; Density topology; Pointwise convergence; -density point; pointwise convergence; pointwise density topology
UR - http://eudml.org/doc/268792
ER -
References
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- [7] Poreda W., Wagner-Bojakowska E., Wilczy´ nski W., A category analogue of the density topology, Fund.Math. 1985, 125, 167-173. Zbl0613.26002
- [8] Wilczy´ nski W., Aversa V., Simple density topology, Rend. Circ. Mat. Palermo (2), 2004, 53, 344-352. Zbl1194.26002
- [9] Wilczy´ nski W., Density topologies, Scientific Bulletyn Of Chełm Section of Mathematics And Computer Science, 2007, 1, 223-227.
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