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 to an open subset of . The former points are the interior points of .
- The interior of , denoted , 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. |