Pre-Closed Set and Pre-Open Set in a Topological Space

Abstract

Mathematics has played a significant role in the development of all   fields of life. It is a science which started   with the beginning of life and has provided tools for  the development of all sciences. We  use the concepts of mathematics  from day to day life to  higher levels of research in almost every field such as transportation,  architecture, medical science, or space science, etc. Thus mathematics has truly acted as the mother of all sciences and nourished their offspring with its concepts.