Some Generalized Covering and Separation Axioms in Topological and Bitopological Spaces

Abstract

As the application of general topology mainly depends upon the properties of open sets and closed sets, topologists have given several generalizations of these concepts. The separation axioms on these classes of open sets have always been proved quite useful in various fields. Still with the emergence of new fields and newer branches, there always remains a scope for the development of new open sets so that new separation axioms and covering properties can be defined over them. In the light of this, here, in this work, we introduce a bunch of new concepts. Development of some generalized open and closed sets both on topological and bitopological spaces are taken into account primarily. Alongside, we generalize the well-known covering properties and separation axioms on the newly found generalized open and closed sets. Moreover, we develop some new separation axioms both on topological and bitopological spaces and explore them. The natural emergence of topological spaces and bitopological spaces from metric spaces and quasi-metric spaces respectively. Various concepts developed in the fields of topological and bitopological spaces by notable mathematicians have been quoted which serve as the motivation of the concepts developed over here. In addition to that, some prominent definitions and results have been recalled which have been used as fundamentals throughout this research work. newline