An Approach to Change the Topology of a Topological Space

Abstract

In this paper, we are going to introduce an approach to convert the topology of a topological space to another topology (in fact, a coarser topology). For this purpose, we consider a topological space $(X, \tau)$ with a closed point $p$ of its points. Using a grill $\mathcal{G}$ on the space $(X, \tau)$ and the closure operator associated with $\tau$, we define a Kuratowski closure operator $cl^*_p$ on $X$ to create the desired topology. We then characterize the form of this resulting topology and also determine its relationship to the initial topology of the space.

Keywords

• kuratowski closure operator
• grill
• coarster topology
• extension topology
• one-point extension topology