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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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