Document Type : Research Paper

Authors

• Amin Talabeigi ¹
• Maryam Talabeigi ²

¹ Department of Mathematics, Payame Noor University(PNU), P.O.Box, 19395-4697, Tehran, Iran.

² Department of Electrical Computer Engineering, instructor of girls Kosar Sirjan branch, Technical and Vocational University (TVU), Kerman, Iran.

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