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arXiv · 1903.11564

Approximation by piecewise-regular maps

Marcin Bilski·Wojciech Kucharz
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Abstract

A real algebraic variety W of dimension m is said to be uniformly rational if each of its points has a Zariski open neighborhood which is biregularly isomorphic to a Zariski open subset of R^m. Let l be any nonnegative integer. We prove that every map of class C^l from a compact subset of a real algebraic variety into a uniformly rational real algebraic variety can be approximated in the C^l topology by piecewise-regular maps of class C^k, where k is an arbitrary integer greater than or equal to l. Next we derive consequences regarding algebraization of topological vector bundles.

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Marcin Bilski, Wojciech Kucharz. 2019-03-27. Approximation by piecewise-regular maps. https://arxiv.org/abs/1903.11564

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