Tubular neighborhood

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In mathematics, a tubular neighborhood of a submanifold of a smooth manifold is an open set around it resembling the normal bundle.

More precisely, if M′ is a submanifold of M, and N is the normal bundle of M′ in M, then a tubular neighborhood of M′ is an extension j of the inclusion map

i:M′ → M

to N, via the inclusion map of M′ into N as the zero section of N, in such a way that j becomes a homeomorphism onto its image.

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