I'm looking for a formal mathematical definition and a proof to the fact that every continent (or an island) has a Continental Divide Line.
Should I assume a terrain is a continues function from R^2 to R (The height function)? A continent or an island is a closed segment within R^2, with height(x,y)=0 for all points along the border, height(x,y)>0 for all points in the continent, and height(x,y)=0 for all points outside the continent?
I'm thinking an "ocean" is a segment on the border.
Intuitively I know what the divide line is, but since it can go "crazy", I'm not sure how to define it.
Can this phenomenon be extended to any manifold in a topological space?