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Turkish Journal of Mathematics

Abstract

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.

DOI

10.55730/1300-0098.3482

Keywords

Ideal topological space, local function, local closure function, $\theta$-open sets

First Page

2086

Last Page

2097

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