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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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