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A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.
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Every manifold can be cut into cubes
Since the environment of this theorem is Stokes theorem and integration on manifolds (Greens theorem and planar regions in this specific case), I would also expect the condition that the smooth maps of …