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; T) and a grill G on the space, we use the closure operator cl associated withT, 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.

کلیدواژه ها:

Kuratowski closure operator ، Kuratowski closure axioms ، grill ، D-topology ، D-space