General topology Basic notions: open sets, neighbourhoods, bases Concept
Closure
Summary
The closure of a subset of a topological space is the intersection of all closed sets that contain it. It is the smallest closed set that contains the subset. In a metric space, it is the set of limits of convergent sequences of points of the subset.
Where this leads
27 pages build on this one.
- Completely normal space
- Ratner's theorems
- Eilenberg–Steenrod axioms
- Particular point topology
- Closable operator
- Generic point
- Specialization preorder
- Regular open set
- Excluded point topology
- Compact operator
- Extremally disconnected space
- Closure of an operator
- Straszewicz's theorem
- Arens–Fort space
- Kuratowski closure axioms
- Net
- Bipolar theorem
- Fréchet–Urysohn space
- Derived set
- Raghunathan's conjecture
- Orientation of a manifold
- Sober space
- Minkowski–Carathéodory theorem
- Choquet theory
- Kuratowski's closure-complement problem
- Krein–Milman theorem
- Excision theorem
Further reading
- Web https://en.wikipedia.org/wiki/Closure_(topology), lead section
About this page
| Tag | 0QEAJB91GZ |
|---|---|
| URI | m2://0QEAJB91GZ |
| Aliases | closure-of-a-set |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54A05 |
| Same as |
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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
- Completely normal space
- Ratner's theorems
- Eilenberg–Steenrod axioms
- Particular point topology
- Closable operator
- Generic point
- Specialization preorder
- Regular open set
- Excluded point topology
- Compact operator
- Extremally disconnected space
- Closure of an operator
- Straszewicz's theorem
- Arens–Fort space
- Kuratowski closure axioms
- Net
- Bipolar theorem
- Fréchet–Urysohn space
- Derived set
- Raghunathan's conjecture
- Sober space
- Kuratowski's closure-complement problem
- Krein–Milman theorem
- Excision theorem