Yes, but can it be segmented in open regions which are homeo/diffeomorphic to subsets of the R²? (Canonical example: the Earth is a three-dimensional object, b

Yes, but can it be segmented in open regions which are homeo/diffeomorphic to subsets of the R²? (Canonical example: the Earth is a three-dimensional object, but looks 2D locally (at a neighborhood of any given point).