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$C^m$ Semialgebraic Sections Over the Plane
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classification
math.CAmath.AGmath.CVmath.LO
keywords
semialgebraicmathbbmathcalsectionbundlecaseconjecturefollowing
abstract
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 $\mathcal{H}$ be a semialgebraic bundle with respect to $C^m_{loc}\left( \mathbb{R}^{2},\mathbb{R}^{D}\right) .$ If $\mathcal{H}$ has a section, then it has a semialgebraic section.
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