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# Approximation of smooth maps by real algebraic morphisms

Published:1997-12-01
Printed: Dec 1997
• Wojciech Kucharz
• Kamil Rusek
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## Abstract

Let $\Bbb G_{p,q}(\Bbb F)$ be the Grassmann space of all $q$-dimensional $\Bbb F$-vector subspaces of $\Bbb F^{p}$, where $\Bbb F$ stands for $\Bbb R$, $\Bbb C$ or $\Bbb H$ (the quaternions). Here $\Bbb G_{p,q}(\Bbb F)$ is regarded as a real algebraic variety. The paper investigates which ${\cal C}^\infty$ maps from a nonsingular real algebraic variety $X$ into $\Bbb G_{p,q}(\Bbb F)$ can be approximated, in the ${\cal C}^\infty$ compact-open topology, by real algebraic morphisms.
 MSC Classifications: 14P05 - Real algebraic sets [See also 12Dxx, 13P30] 14P25 - Topology of real algebraic varieties