Further study of topological and ideal topological spaces

Abstract

The thesis consists of Six Chapters, the details of which are given below. A general introduction, definition of the problem, methodology and objectives of the research work are presented in the First Chapter. In the Chapter 2, we introduce the new notion called and#960;g-locally closed sets in topological spaces. Also we define and#2024;gl-continuous and and#960;gl-irresolute functions. Properties of such new sets and functions are obtained on the line of research. In the Chapter 3, we define and study some new generalized locally closed sets. Further some new subsets of topological spaces are introduced and studied in detail. Some decomposition theorems are given. In the Chapter 4, the concept of and#955;-closed sets was introduced in the field of topological spaces. Generalization of and#955;-closed sets has been studied in detail. Some important theorems are obtained. Examples and counter examples are given to substantiate the concept in the thesis. In the Chapter 5, generalized and#61559; -open sets are defined and studied. Some new ideal topological subsets are defined and introduced in and#61559; -topological spaces. A new space called and#61559; -*-extremally disconnected space have been introduced and discussed. Some decompositions of and#61559; -continuity via idealization are given. In the Chapter 6, we presented the conclusion by researching generalizations of closed sets, some new separation axioms have been founded and they turn out to be useful in the study of digital topology newline