In this paper we work on preserving various types of continuity in ideal topological spaces. The accent will be on $\theta$-continuity and weak continuity. We will give their translations in ideal topological spaces. As a consequence of those results, we will prove that every $\theta$-continuous function is continuous if topologies are generated by $\theta$-open sets and we will give an example of a weakly continuous function which is not $\tau_\theta$-continuous. This will complete the diagram of relations between continuous, $\tau_\theta$-continuous, $\theta$-continuous, weakly continuous, and faintly continuous functions.
Ideal topological space, local function, local closure function, $\theta$-open sets
NJAMCUL, ANIKA and PAVLOVI?, ALEKSANDAR
"Various types of continuity and their interpretations in ideal topological spaces,"
Turkish Journal of Mathematics: Vol. 47:
7, Article 16.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss7/16