On generalization of the $\mathcal{T}_{A_{I}}-$density topology
Abstract
We present a further generalization of the $\mathcal{T}_{A_{I}}$-density
topology introduced in (Wojciech Wojdowski, A category analogue of the
generalization of Lebesgue density topology, Tatra Mt. Math. Publ., 42
(2009), 11-25 ) as a generalization of the $I-$density topology. We
construct 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 several
basic properties of the topologies.
topology introduced in (Wojciech Wojdowski, A category analogue of the
generalization of Lebesgue density topology, Tatra Mt. Math. Publ., 42
(2009), 11-25 ) as a generalization of the $I-$density topology. We
construct 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 several
basic properties of the topologies.