Difference between revisions of "Manifold"
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An ''n''-dimensional complex manifold ''N'' is a [[topological space]] such that every point in ''N'' has a neighbourhood that is [[homeomorphism|homeomorphic]] to '''C'''<sup>''n''</sup>. | An ''n''-dimensional complex manifold ''N'' is a [[topological space]] such that every point in ''N'' has a neighbourhood that is [[homeomorphism|homeomorphic]] to '''C'''<sup>''n''</sup>. | ||
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| + | Manifolds are [[Hausdorff space|Hausdorff]] and [[2nd-countable space|2nd-countable]]. | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
[[category: Topology]] | [[category: Topology]] | ||
Revision as of 05:31, April 12, 2007
The Möbius strip is an example of a 2-manifold.
An n-dimensional manifold (or n-manifold) M is a topological space such that every point in M has a neighbourhood that is homeomorphic to Rn.
An n-dimensional complex manifold N is a topological space such that every point in N has a neighbourhood that is homeomorphic to Cn.
Manifolds are Hausdorff and 2nd-countable.