General topology Compactness Concept
Open cover
Summary
An open cover of a subset of a topological space is a family of open sets whose union contains the subset. Open covers are used to define compactness.
Where this leads
16 pages build on this one.
- Moore space
- Stone's theorem on paracompactness of metric spaces
- Lebesgue covering dimension
- Countably compact space
- Homotopy group with coefficients
- Lindelöf space
- Lusternik–Schnirelmann category
- Metacompact space
- Cartier divisor
- Partition of unity
- Topological entropy
- Alexander subbase theorem
- Nerve of a cover
- Nerve theorem
- Čech cohomology
- Paracompact space
Further reading
About this page
| Tag | 049PXYHW1T |
|---|---|
| URI | m2://049PXYHW1T |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54D30 |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Moore space
- Stone's theorem on paracompactness of metric spaces
- Lebesgue covering dimension
- Countably compact space
- Lindelöf space
- Lusternik–Schnirelmann category
- Metacompact space
- Cartier divisor
- Partition of unity
- Topological entropy
- Alexander subbase theorem
- Nerve of a cover
- Nerve theorem
- Čech cohomology
- Paracompact space