<abstract xmlns="http://www.w3.org/1999/xhtml"> Analogously to the method used for c-density point, we introduce the notion of cμ-density point for arbitrary set A having the Baire property, replacing the convergence in measure with the convergence with respect to the σ-ideal of microscopic sets. Then, we consider the density type topology Tcμ generated by cμ-density operator and study basic properties of Tcμ in comparison with the classical density, I-density and c-density topologies</abstract>

Analogously to the method used for c-density point, we introduce the notion of cμ-density point for arbitrary set A having the Baire property, replacing the convergence in measure with the convergence with respect to the σ-ideal of microscopic sets. Then, we consider the density type topology Tcμ generated by cμ-density operator and study basic properties of Tcμ in comparison with the classical density, I-density and c-density topologies

Density topology involving microscopic sets and category

University of Łódź Faculty of Mathematics and Computer Science Banacha 22 PL-90-238 Łódź POLAND

Institute of Mathematics Technical University of Łódź Wólczanska 215 PL-90-924 Łódź POLAND

Tatra Mountains Mathematical Publications

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

{"article-title":"Density topology involving microscopic sets and category"}

Analogously to the method used for c-density point, we introduce the notion of cμ-density point for arbitrary set A having the Baire property, replacing the...

Density topology involving microscopic sets and category

Publié en ligne: 25 sept. 2015

Pages: 113 - 132

Reçu: 10 oct. 2014

DOI: https://doi.org/10.1515/tmmp-2015-0009

© 2015

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