A function which is arc-analytic but not continuous

Bierstone, E.; Milman, P. D.; Parusiński, A.

doi:10.1090/S0002-9939-1991-1072083-4

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A function which is arc-analytic but not continuous
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by E. Bierstone, P. D. Milman and A. Parusiński

Proc. Amer. Math. Soc. 113 (1991), 419-423

DOI: https://doi.org/10.1090/S0002-9939-1991-1072083-4

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Abstract:

We construct an arc-analytic function (i.e., a function analytic on every real analytic arc) which is not continuous, as well as a continuous arc-analytic function which is not subanalytic.

References

Edward Bierstone and Pierre D. Milman, Arc-analytic functions, Invent. Math. 101 (1990), no. 2, 411–424. MR 1062969, DOI 10.1007/BF01231509