On topology expansion using ideals

Abstract

Topologies can be expanded with the help of ideals, using the local function, an operator resembling the closure of a set. The aim of this paper is to define the ideals which enable us to create this topology ${\tau }^{\ast }$ on $X$ simultaneously making a specific set $A\subseteq X$ open in ${\tau }^{\ast }$. We study certain properties of ${\tau }^{\ast }$, especially under the assumption that $A$ is a preopen set. Further, we reflect on the ideal topological space in which the ideal is generated by a chosen family of dense sets. Here we prove that the generated topology by this ideal is submaximal, but not maximal connected.

7 pages