# Tubular neighbourhood style theorem reference request

Let $X$ be a smooth manifold and $Y$ be a closed submanifold. Then there exists a neighbourhood $U$ of $Y$ in $X$ such that $Y$ is a deformation retract of $U$ right?

I can only find (stronger forms of) this in literature under the assumption that $Y$ is compact, which I don't think is necessary for the above statement. So what would be a reference?

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Thanks for the reference. I am a bit confused. Does Kosinski say that in my situation $U$ can even be choosen diffeomorphic to the normalbundle of $Y$ in $X$? –  Jan Mar 14 '12 at 18:55