topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

, a branch of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, a collar neighbourhood of a

manifold with boundary In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...

M

is a

neighbourhood A neighbourhood (Commonwealth English) or neighborhood (American English) is a geographically localized community within a larger town, city, suburb or rural area, sometimes consisting of a single street and the buildings lining it. Neighbourh ...

of its boundary

M

that has the same structure as

\partial M \times differentiable manifold with boundary, U \subset M is a ''collar neighbourhood'' of M whenever there is a diffeomorphism">differentiable manifold">differentiable manifold with boundary, U \subset M is a ''collar neighbourhood'' of M whenever there is a diffeomorphism f : \partial M \times [0, 1) \to U such that for every x \in \partial M, f (x, 0) = x . Every differentiable manifold has a collar neighbourhood.

References

{{topology-stub Differential topology Manifolds