Abstract
Let \(\mathbb {K}\) be an uncountable field of characteristic zero and let f be a function from \(\mathbb {K}^n\) to \(\mathbb {K}\). We show that if the restriction of f to every affine plane \(L\subset \mathbb {K}^n\) is regular, then f is a regular function.
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Acknowledgements
This paper is a positive answer to the question of Wojciech Kucharz, which was presented to us in private communication. We would like to thank Wojciech Kucharz for his valuable remarks.
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Gryszka, B., Gwoździewicz, J. On some regularity condition. Period Math Hung 86, 336–342 (2023). https://doi.org/10.1007/s10998-022-00476-4
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DOI: https://doi.org/10.1007/s10998-022-00476-4