No compact manifold has a single Euclidean chart
= No compact manifold has a single Euclidean chart
A nonempty compact manifold cannot be homeomorphic to an open subset of Euclidean space, since no nonempty Euclidean open set is compact.
= No compact manifold has a single Euclidean chart
A nonempty compact manifold cannot be homeomorphic to an open subset of Euclidean space, since no nonempty Euclidean open set is compact.