Cantor tree surface

In dynamical systems, the Cantor tree is an infinite-genus surface homeomorphic to a sphere with a Cantor set removed.

The blooming Cantor tree is a Cantor tree with an infinite number of handles added in such a way that every end is a limit of handles.

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The bark of a fractal tree, splitting in two directions at each branch point, forms a Cantor tree surface. Drilling a hole through the tree at each branch point would produce a blooming Cantor tree.

An Alexander horned sphere . Its non-singular points form a Cantor tree surface.