An approach to change the topology of a topological space with the help of its closed sets in the presence of grills

The aim of this paper is introduce an approach to convert thetopology of a topological space to another topology (in fact, a coarser topology).For this purpose, considering a closed set P of subsets of a topological space(𝑋; τ) and a grill 𝒢 on the space, we use the closure operator 𝑐𝑙 associated with τ, to define a new Kuratowski closure operator 𝑐𝑙*𝑃 on 𝑋. The operator 𝑐𝑙*𝑃 induces the desired topology. We then characterize the form of this resultingtopology and also determine its relationship to the initial topology of the space. Some examples are given. Also, using a suitable grill in the method, we converteach topological space to corresponding 𝐷-space.