### A generalization of the C−density topology

#### Abstract

We present a fgeneralization of the $\mathcal{T}_{c}-$density topology

introduced in \cite{wo5} as a topology ivolving both a category and measure

approach to the notion of density. We construct an ascending sequence $

\left\{ \mathcal{T}_{\mathcal{A}_{c\left( n\right) }}\right\} _{n\in

\mathbb{N} }$ of density topologies which leads to the $\mathcal{T}_{\mathcal{A}_{c\left( \omega \right) }}-$density topology including all previous

topologies. We examine several basic properties of the topologies.

introduced in \cite{wo5} as a topology ivolving both a category and measure

approach to the notion of density. We construct an ascending sequence $

\left\{ \mathcal{T}_{\mathcal{A}_{c\left( n\right) }}\right\} _{n\in

\mathbb{N} }$ of density topologies which leads to the $\mathcal{T}_{\mathcal{A}_{c\left( \omega \right) }}-$density topology including all previous

topologies. We examine several basic properties of the topologies.

#### Full Text:

PDFDOI: https://doi.org/10.2478/tatra.v62i0.273