Idealization of Ganster-Reilly decomposition theorems

TL;DR

This paper extends Ganster and Reilly's 1990 decomposition of continuity using ideals, showing that a function's continuity can be characterized by pre-I-continuity and I-LC-continuity, and provides a decomposition of I-continuity.

Contribution

It generalizes the classical decomposition of continuity to the context of ideals, offering new characterizations of I-continuity.

Findings

Characterization of I-continuity via pre-I-continuity and I-LC-continuity

Extension of Ganster-Reilly decomposition to ideal-based frameworks

New decomposition results for I-continuity

Abstract

In 1990, Ganster and Reilly proved that a function is continuous if and only if it is precontinuous and LC-continuous. In this paper we extend their decomposition of continuity in terms of ideals. We show that a function $f \colon (X,\tau,{\cal I}) \to (Y,\sigma)$ is continuous if and only if it is pre-I-continuous and I-LC-continuous. We also provide a decomposition of I-continuity.