@article { author = {Talabeigi, Amin and Talabeigi, Maryam}, title = {An Approach to Change the Topology of a Topological Space}, journal = {Sahand Communications in Mathematical Analysis}, volume = {19}, number = {3}, pages = {55-63}, year = {2022}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2022.132038.842}, 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}, url = {https://scma.maragheh.ac.ir/article_254339.html}, eprint = {https://scma.maragheh.ac.ir/article_254339_7e881e561c422471177c3588c1ac0ca6.pdf} }