Manifold Atlas:Definition of “manifold”
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This page defines the term “manifold” as used in the Manifold Atlas.
1 Definition
We assume that all manifolds are of a fixed dimension n. An n-dimensional manifold is a second countable Hausdorff space for which every point has a neighbourhood homeomorphic to an open subset of or an open subset of . The former points are the interior points of .
- The interior of , denoted
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is the subset of points for which . - The boundary of , written , is the compliemnt of the interior of
- is called closed if is compact and is empty.
Extra structures
Typically, but not necessarly, the word ``manifold`` will mean as above with extra structure. The extra structure may or may not be emphasised in notation and vocabulary.
- A smooth manifold is a manifold with an equivalence class of
2 References
This page has not been refereed. The information given here might be incomplete or provisional. |