Suppose $M$ is a smooth manifold and $S$ a smooth embedded submanifold of $M$. Does there exist an open neighborhood $U$ of $S$ and a smooth map $U\to S$ which is a retraction?
2026-03-25 06:07:07.1774418827
Does there exist an open neighborhood $U$ of $S$ and a smooth map $U\to S$ which is a retraction?
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Take a tubular neigborhood $U$ of $S$ (consult a book on differential topology; see also https://en.wikipedia.org/wiki/Tubular_neighborhood). This contains $S$ as a strong deformation retract.