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Spaces of rational maps and the Stone-Weierstrass theorem. (English) Zbl 1086.58005
Summary: It is shown that Segal’s theorem on the spaces of rational maps from $$\mathbb C$$P$$^{1}$$ to$$\mathbb C$$P$$^{n}$$ can be extended to the spaces of continuous rational maps from $$\mathbb C$$P$$^{m}$$ to $$\mathbb C$$P$$^{n}$$ for any $$m \leq n$$. The tools are the Stone-Weierstrass theorem and Vassiliev’s machinery of simplicial resolutions.

##### MSC:
 58D15 Manifolds of mappings 55P10 Homotopy equivalences in algebraic topology
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