Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Idealization of Ganster-Reilly decomposition theorems   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.

13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
1
The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
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The categories of this paper are: stat