Collar neighbourhood
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,.
Since is diffeomorphic to, it is equivalent to take a diffeomorphism.
Every differentiable manifold has a collar neighbourhood.