- #1

jgens

Gold Member

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I realize the Collar Neighborhood Theorem essentially provides the desired map, but I am actually using this result to prove the aforementioned theorem. My thought on how to prove the theorem is to show local existence, show that you can locally extend a retraction, and then use Zorn's Lemma to construct a neighborhood retraction of the boundary. The only difficulty I run into here is showing local extendability. Can anyone help me with this step?