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Results tagged with function-spaces
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user 46510
2
votes
Accepted
The set of embeddings is open in the strong Whitney topology
A proof of this is also contained in Michor: Manifolds of mappings. There Proposition 5.3 establishes that the $C^r$-embeddings are $WO^1$ open in the space $C^r (M,N)$ (no restriction on the manifold …
- 2,388
6
votes
Accepted
Is $π:\mathcal{C}^∞(M,N)→\mathcal{C}^∞(S,N)$, $π(f)=f|_S$ a quotient map in the $\mathcal{C}...
Let me try to give at least some partial answers (and apologies that I am leaving the realm of topological spaces to give you these answers, but I am a differential geometer, so you have been warned): …
- 2,388