# Tame submanifold

From Topospaces

*This article defines a property of a submanifold inside a manifold*

## Definition

Let be a manifold of dimension and a submanifold of dimension . Then is termed *tame* in if for every point , there exists a neighbourhood of in such that the pair is homeomorphic to the pair where is viewed as a linear subspace of .

Another way of saying this is that the local codimension at each point, equals the codimension of the submanifold as a whole.

## Facts

An example of a submanifold which is *not* tame is the Alexander horned sphere in .