A study on new kind of closed sets and their properties in the topological spaces

Abstract

In 1937, M.H stone introduced regular open sets in topological spaces newlineand the complement as regular closed sets. In 1963 N. Levine introduced semi newlineopen sets in Topological spaces. The same author introduced generalized closed newlinesets in 1970. Since then many authors focused on this areana in which i have newlineindulged to bring out new types of closed sets in Topological spaces. Mainly, newlinethis thesis aims to introduce new kinds of generalized closed sets and open sets. newlineThe concept of continuity, homeomorphism, connectedness, compactness and newlineseparation axioms are discussed for the newly defined closed sets. newlineIn the first chapter some important definitions and results from existing newlineliterature, which are essential for the development of the thesis are given. newlineSecond chapter introduces the new closed sets namely (r*g*)*-closed sets and newlinetheir properties. In chapter III, the concept of continuity, irresoluteness and newlinehomeomorphism of (r*g*)*-closed set are discussed. Chapter IV focuses on newlinethe concept of (r*g*)*-connectedness and (r*g*)*-compactness. Chapter V and newlineVI deal with (r*g*)*-separation axioms. Finally chapter VII is devoted to the newlinenotion of (r*g*)*-locally closed set. newline