𝐶𝑚 semialgebraic sections over the plane
2022 年 74 巻 3 号 p. 759-811
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2022 年 74 巻 3 号 p. 759-811
In this paper we settle the two-dimensional case of a conjecture involving unknown semialgebraic functions with specified smoothness. More precisely, we prove the following result: Let ℋ be a semialgebraic bundle with respect to 𝐶^{𝑚}_{𝑙𝑜𝑐}(ℝ2, ℝ𝐷). If ℋ has a section, then it has a semialgebraic section.
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