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Tubular Neighborhood

The tubular embedding of a Submanifold $M^m\subset N^n$ of another Manifold $N^n$ is an Embedding $t:M\times\Bbb{B}^{n-m}\to N$ such that $t(x,0)=x$ whenever $x\in M$, where $\Bbb{B}^{n-m}$ is the unit Ball in $\Bbb{R}^{n-m}$ centered at 0. The tubular neighborhood is also called the Product Neighborhood.

See also Ball, Embedding, Product Neighborhood


Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 34-35, 1976.

© 1996-9 Eric W. Weisstein