We present a further generalization of the $\mathcal{T}_{A_{I}}$-densitytopology introduced in (Wojciech Wojdowski, A category analogue of thegeneralization of Lebesgue density topology, Tatra Mt. Math. Publ., 42(2009), 11-25 ) as a generalization of the $I-$density topology. Weconstruct an ascending sequence $\{\mathcal{T}{_{A_{I(n)}}\}}_{n\in \mathbb{N%}}$ of density topologies which leads to the $\mathcal{T}_{A_{I(\omega )}}$%-density topology including all previous topologies. We examine severalbasic properties of the topologies.
@article{407,
title = {On generalization of the $\mathcal{T}\_{A\_{I}}-$density topology},
journal = {Tatra Mountains Mathematical Publications},
volume = {68},
year = {2017},
language = {EN},
url = {http://dml.mathdoc.fr/item/407}
}
Krzeszowiec, Alicia; Wojdowski, Wojciech. On generalization of the $\mathcal{T}_{A_{I}}-$density topology. Tatra Mountains Mathematical Publications, Tome 68 (2017) . http://gdmltest.u-ga.fr/item/407/