Knapp, Anthony W. Department of Mathematics, State University of New York, Stony Brook, New York.
Last reviewed:June 2020
- Differentiable structure
- Other structures
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A Hausdorff topological space with an n-dimensional atlas of charts for some integer n. The integer n is called the dimension of the manifold. If M is a Hausdorff space, an n-chart on M is a pair (U, ϕ) with U an open subset of M and ϕ a homeomorphism of U onto an open subset ϕ(U) of n-dimensional euclidean space R n. An n-dimensional atlas for M is a system of n-charts (U, ϕ) such that the union of the sets U is all of M. See also: Topology
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