Manifold: Difference between revisions
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==Definition== | ==Definition== | ||
A [[topological space]] is said to be a '''manifold''' if | A [[topological space]] is said to be a '''manifold''' if it satisfies the following equivalent conditions: | ||
* It is [[Hausdorff space|Hausdorff]] | |||
* It is [[second countable space|second countable]] | |||
* Every point has a neighbourhood that is homeomorphic to some open set in Euclidean space. If the topological space is connected, the dimension of the Euclidean space is the same for all points | |||
Revision as of 14:32, 22 May 2007
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
Definition
A topological space is said to be a manifold if it satisfies the following equivalent conditions:
- It is Hausdorff
- It is second countable
- Every point has a neighbourhood that is homeomorphic to some open set in Euclidean space. If the topological space is connected, the dimension of the Euclidean space is the same for all points