On soft separation axioms and a new class of soft closed sets in soft tech closure

Abstract

This thesis deals with the concepts of the lower separation axioms T0-space, newlineT1-space, T2-space, Pseudo Hausdorff and Uryshon space in soft Cand#711;ech closure newlinespaces and characterized the higher separation axioms such as soft quasi newlineregular, soft semi regular, soft pseudo regular, soft regular, soft semi normal, soft newlinenormal and completely soft normal. Also, the postulates of R0, R1-spaces and the newlinerelationship between R0, R1 and lower separation axioms in soft Cand#711;ech closure newlinespaces are characterized. Also, characterization of soft separated sets, soft newlineconnectedness, soft feebly disconnectedness and local soft connectedness are newlineestablished. The concepts of a new class of soft generalized closed sets and newlinesoft and#8706;-closed sets are introduced. Also investigate the behavior relative to union, newlineintersection and soft subspaces of soft g-closed and soft and#8706;-closed sets as well as soft newlineg-open sets. In the study of soft g-closed sets and soft and#8706;-closed sets, a new type newlineof separation axioms namely T 1 newline2 newline, T newline0 newline1 newline2 newlineand T newline00 newline1 newline2 newlinespaces introduced and discussed the newlinerelationship among them. Basic properties in stronger form of soft g-closed, newlinesoft and#8706;-closed, soft g newlineand#8727;and#8727;-closed sets and in and#945;gs-closed sets are characterized. The newlinenotions of lower separation axioms such as pairwise T0-space, pairwise T1-space, newlinepairwise T2-space, pairwise Pseudo Hausdorff and pairwise Uryshon space in soft newlinebiCand#711;ech closure spaces are studied and also characterized the higher separation newlineaxioms namely pairwise soft quasi regular, pairwise soft semi regular,pairwise soft Pseudo regular, pairwise soft regular, pairwise soft normal and newlinepairwise completely soft normal. The concepts of pairwise soft separated sets, newlinepairwise soft connectedness and pairwise soft feebly disconnectedness are newlineintroduced. The relation between the pairwise connectedness in the soft biCand#711;ech newlineclosure space (FA, k1, k2) and that of the associated soft bitopological spaces newline(FA, and#964;1, and#964;2) is established. The possibility of the extension of some important newlinetheorems in Cand#711;ech and biCand#711;ech closure spaces has been