A topological space M is called an m-dimensional manifold (or m-manifold) if every point of M has a neighborhood homeomorphic to an open subset of R m . Since one can clearly take this subset to be an open ball, and since an open ball in R m is homeomorphic to R m itself, the condition for a space to be a manifold can also be expressed by saying that every point has a neighborhood homeomorphic to R m .
KeywordsOpen Subset Topological Space Tangent Vector Complex Manifold Smooth Manifold
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