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.