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Idealization of Ganster-Reilly decomposition theorems

Julian Dontchev
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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 $f \colon (X,τ,{\cal I}) \to (Y,σ)$ is continuous if and only if it is pre-I-continuous and I-LC-continuous. We also provide a decomposition of I-continuity.

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Julian Dontchev. 1999-01-05. Idealization of Ganster-Reilly decomposition theorems. https://arxiv.org/abs/math/9901017

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