Tame submanifold

Definition
Let $$M$$ be a manifold of dimension $$m$$ and $$N$$ a submanifold of dimension $$n$$. Then $$N$$ is termed tame in $$M$$ if for every point $$x \in N$$, there exists a neighbourhood $$U$$ of $$x$$ in $$M$$ such that the pair $$(U, U \cap N)$$ is homeomorphic to the pair $$(\R^m,\R^n)$$ where $$\R^n$$ is viewed as a linear subspace of $$\R^m$$.

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 $$\R^3$$.