Study on Generalized Topological Space

Abstract

The aim of the thesis is to extend the study of the properties of some newlinesubsets in an ideal topological spaces, the generalized topological space and newlinegeneralized topological spaces via hereditary classes.In an ideal topological space (X; t; I ), if N = fA_ Xjint(cl(A)) =/0g; N _ =fA_Xjint_(cl(A))= /0g and N1 =fA_Xjint_(cl_(A))= /0g; first westudy the relation between the family of sets N ;N _ and N1 and discuss someof their properties. Also, we give a characterization of codense ideals in termsof this sets.Next, we define the extension of two hereditary classes in aGeneralized Topological Spaces (GTS) and _k and#1048576;rare sets. Also, weestablish some properties of _kand#1048576;rare sets and characterizations of completelykand#1048576;codense hereditary class and k_and#1048576;dense sets are given. It is also establishedthat N _k is completely kand#1048576;codense: newline newline