Analogously to the method used for $c-$density point, we introduce thenotion of $c_{\mu }-$density point for arbitrary set $A$ having the Baireproperty, replacing the covergence in measure with the convergence withrespect to the $\sigma -$ideal of microscopic sets.Then we consider the density type topology $\mathcal{T}_{c_{\mu }}$ generated by $c_{\mu }-$ density operator and study basic properties of $\mathcal{T}_{c_{\mu }}$ incomparison with the classical density, $\mathcal{I}-$density and $c-$densitytopologies.
@article{344,
title = {Density topology involving microscopic sets and category},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v62i0.344},
language = {EN},
url = {http://dml.mathdoc.fr/item/344}
}
Wagner-Bojakowska, Elżbieta; Wilczyński, W.; Wojdowski, W. Density topology involving microscopic sets and category. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v62i0.344. http://gdmltest.u-ga.fr/item/344/