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单词 Compact Manifold
释义

Compact Manifold

A Manifold which can be ``charted'' with finitely many Euclidean Space charts. The Circle is the onlycompact 1-D Manifold. The Sphere and -Torus are the only compact 2-D Manifolds. It is an open question if the known compact Manifolds in 3-D are complete, and it is not even known whata complete list in 4-D should look like. The following terse table therefore summarizes current knowledge about the numberof compact manifolds of dimensions.

11
22

See also Tychonof Compactness Theorem
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更新时间:2024/11/15 2:21:33