A Study of New Topologies on R.

Abstract

The present dissertation entitled, “A Study of New Topologies on R” comprises certain investigations carried out by me at School of Mathematics, Thapar University, Patiala, under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics, Thapar University, Patiala. The aim of this work is to find new topologies with this new set of basis B− and B+. The topologies generated from this new set of basis are different from standard, lower limit, upper limit and k-topologies. We compared well known topologies with new topologies on R. The whole work is divided into four chapters. Chapter 1 is introduction which includes brief account of definitions and their examples which will be required for the later chapters. In chapter 2, we have studied some main theorems which guarantees how topology can be generated from given base and vice-versa. The aim of chapter 3 is to study well known topologies on R and their topological properties. In chapter 4, we introduced new topologies on real line and compared them with well known topologies on R. At the end of this dissertation, we have bibliography of research papers and books cited in the dissertation.