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Collar neighbourhood

From Wikipedia, the free encyclopedia

In topology, a branch of mathematics, a collar neighbourhood of a manifold with boundary is a neighbourhood of its boundary that has the same structure as .

Formally if is a differentiable manifold with boundary, is a collar neighbourhood of whenever there is a diffeomorphism such that for every , .[1]: p. 222  Every differentiable manifold has a collar neighbourhood.[1]: th. 9.25 

Formally if is a topological manifold with boundary, is a collar neighbourhood of whenever there is an homeomorphism such that for every , .

References

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  1. ^ a b Lee, John (2012), Introduction to Smooth Manifolds, Graduate Texts in Mathematics, vol. 218, Springer, ISBN 9781441999825