For a natural number $n$, do we have a continuous map from the orthogonal group $O(n)$ to the orthogonal group $O(n+1)$ (seen as topological spaces)?
2026-03-28 16:20:03.1774714803
Continuous maps between orthogonal groups
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There is continuous inclusion map: Let $O(n)$ act on $\mathbb{R}^{n+1}$, by ignoring the $(n+1)-$th component and acting on the first $n$ components in the usual way.