Separation Axioms In Fibrewise Ideal Topological Spaces

Abstract

If (X, 𝜏) is a topological space, I is an ideal on X and

𝜏*(I) the topology finer than 𝜏 induced by the ideal I, then for any topological space B with a continuous map p:XB we call (X, 𝜏*(I)) the fibrewise ideal topological space over B with fiber subspaces { Xb : b ∈ B}; where Xb=P-1(b) for all b ∈ B.

The aim of this thesis is to define separation axioms in fibrewise ideal topological spaces and to study some of their basic properties. Also we discuss the main concepts, the important results in the topic including the relationship between these axioms and with the known separation axioms.