The Sphere, $S^2$, has lots of homemorphic embeddings into $\mathbb{R^3}$. But can every single one be deformed back into a sphere from within $\mathbb{R^3}$?
In other words, does each bi-continuous injective $f:S^2 \to \mathbb{R^3}$ have an isotopy $g:f(S^2)\times [0,1] \to \mathbb{R^3}$, where $g(f(S^2)\times\{1\}) = \{(x,y,z): x^2 + y^2 + z^2 = 1\}$?
How about for other manifolds embedded into other euclidean spaces?