A study on some topological concepts in ideal topological spaces

Abstract

The aim of the thesis is to study certain topological concepts in terms of R − I −open sets in ideal topological spaces. First, we developed separation axioms and then weak separation axioms in ideal topological spaces mainly in R − I − spaces. We studied R − I − T i (i = 0, 1, 2) and R − I – R i (i = 0, 1) spaces. We brought in spaces weaker than R − I – R i (i = 0, 1) spaces. We present a new class of sets and functions in supra ideal topological space via supra R − I −open sets. We have surveyed minimal (maximal) R − I −open sets. Later, we extend the notion of R − I −open sets to introduce somewhat R − I − continuous functions, contra R − I − continuous functions, almost contra R − I − continuous functions and investigate certain properties and several characterisations of such concepts. We widen the concept of continuity to set multifunctions in ideal topological space by extending the class of R − I −open sets. We introduce a class of continuous multifunctions namely upper and lower R − I −continuous multifunctions characterisations of the same.