Various types of continuity and their interpretations in ideal topological spaces

Abstract

This paper is a continuation of work started in \cite{njampavcont} on preserving continuity in ideal topological spaces. We will deal with $θ$-continuity and weak continuity and give their translations in ideal topological spaces. As consequences of those results, we will prove that every $θ$-continuous function is continuous if topologies are generated by $θ$-open sets and we will give an example of weakly continuous function which is not $τ_θ$-continuous. This will complete the diagram of relations between continuous, $τ_θ$-continuous, $θ$-continuous, weakly continuous and faintly continuous functions.