A Study On A Weaker Form Of A B Closed Sets And Its Compactness In Topological Spaces

Abstract

Topology is the most innovative branch of mathematics The point newlineset topology is the most basic and conventional division of topology It newlinedelineates the compactness and connectedness of topological spaces newlineTopology is of interest in its own right Also it is the basis for further study newlinein analysis geometry and algebraic topology Topology can be defined as the newlinequalitative properties of certain objects called sets mappings and topological newlinespaces The extension of traditional closed sets to semiopen sets preopen newlinesets generalized closed set open sets and more relevant concepts newlineintroduce the weaker forms of open sets whose complement sets are affiliated newlineto the closed sets The objects which serve to be invariant under certain type newlineof transformations are called continuous maps and these kind of equivalence newlineare called homeomorphism In an immediate insight two spaces of newlinehomeomorphism can be put forth if one can be defined into the other without newlinecutting or gluing Homeomorphism which can be defined as a continuous newlinefunction with a continuous inverse is necessarily more technical newlineThe concept of topological space deals with the study of real line newlineEuclidean spaces and the continuous functions on these spaces Earlier newlineresearches in this area initiated the present research It is the ephimeral newlinemonograph which reconnoitres over the new class of semi generalized bclosed newlinesets that investigate the intersection of the two semi generalized bclosed newlinesets union of two semi generalized bclosed sets and discusses its newlineother properties The present research also studies the separation axioms newlinesemi generalized bclosure operator semi generalized bclosed maps semi newlinegeneralized bopen maps semi generalized bcontinuous function newlineapproximately semi generalized bclosed maps approximately semi newlinegeneralized bopen maps and approximately semi generalized bcontinuous newlinefunctions newlineThe main class of semi generalized bcontinuous which forms the newlinesubclass of semi generalized bcontinuous is precisely determined and the newlineclass of map is closed under the composition of maps