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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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Existence of tubular neighborohoods of locally flat topological embeddings
seq=1#page_scan_tab_contents), theorem 3 gives manifolds embedded in euclidean space with normal bundle an open disk bundle (hence locally flat) without a closed disk sub-bundle. …