A study on weakly semi closed sets in topological spaces

Abstract

Abstract newlineTopological spaces express naturally in mathematical analysis, abstract algebra newlineand geometry. This has made topology one of the great unifying ideas of mathematics. newlineGeneral topology or point-set topology defines and studies some useful properties of newlinespaces and maps, such as connectedness, compactness and continuity. newlineGeneral topology is one of the thrust areas of topology in mathematics. A large newlinenumber of mathematicians have contributed a lot in the development of general topology newlineall over the world. They have used various types of sets to define and study various newlinetypes of topological properties like covering and separation axioms. Side by side, they newlinehave generalized continuity and homeomorphism also according to the requirements. newlineThe primary goal in general topology is to investigate and compare different classes newlineof topological spaces. newlineHere the study is to focus on new type of closed sets namely weakly semi-closed newlinesets in topological spaces. Also we introduce and studied weakly semi open sets newlinevii newlinein topological spaces. In the growth of general topology, investigation of different newlinetypes of generalized closed sets are of much interest for research scholars. We study newlinethe relationship between weakly semi-closed sets and some existing closed sets in newlinetopological spaces. The basic properties of weakly semi-closed sets and weakly semiopen newlinesets have been investigated. Using the concept of continuity, weakly semicontinuous newlinefunctions are introduced and compared with various existing continuous newlinefunctions in topological spaces. The weakly semi-closed maps, weakly semi-open newlinemaps and weakly semi- homeomorphisms in topological spaces are also introduced newlineand investigated. Further, we study and investigate a new class of separation axioms newlinenamely ws and#1048576; Tk spaces (k = 0; 1; 2). Also, basic properties of these separation newlineaxioms are discussed. Using the concept of weakly semi- open sets and weakly semiclosed newlinesets, weakly semi-regular space and weakly semi-normal spaces in topological newlinespaces have been introduced an