Approximation of smooth maps by real algebraic morphisms

http://dx.doi.org/10.4153/CMB-1997-054-x
Canad. Math. Bull. 40(1997), 456-463

  Published:1997-12-01
 Printed: Dec 1997

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.