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Analytic functions are \({\mathcal I}\)-density continuous. (English) Zbl 0826.26011
The \({\mathcal I}\)-density continuous functions are those functions \(f: \mathbb{R}\to \mathbb{R}\) which are continuous when the domain and the range are equipped with the \({\mathcal I}\)-density topology introduced by the reviewer. If \(f: \mathbb{R}\to \mathbb{R}\) is analytic, then it is \({\mathcal I}\)-density continuous. However, there exists a \(C^\infty\) and convex function which is not \({\mathcal I}\)-density continuous.

MSC:
26E05 Real-analytic functions
26A21 Classification of real functions; Baire classification of sets and functions
26E10 \(C^\infty\)-functions, quasi-analytic functions
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