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I'm looking for a reference or a proof of the following statement :

Let $M$ be a compact smooth manifold with boundary, . Then the space of embeddings $\partial M\times[0,1]\to M$ inducing the identity $\partial M\times{0}\to \partial M$ is contractible.

3 edited body; added 22 characters in body

I'm looking for a reference or a proof of the following statement :

Let $M$ be a compact smooth manifold with boundary, the space of embeddings $\partial M\times[0,1)\to M\times[0,1]\to M$ inducing the identity on the boundary $\partial M\times{0}\to \partial M$ is contractible.

2 added 8 characters in body

I'm looking for a reference or a proof of the following statement :

Let $M$ be a compact smooth manifold with boundary, the space of embeddings $\partial M\times[0,1)\to M$ inducing the identity on the boundary is contractible.

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