General topology Metric spaces Concept
Complete metric space
Summary
A complete metric space is a metric space in which each Cauchy sequence converges to a point of the space. The real numbers are complete, and the rational numbers are not.
Where this leads
22 pages build on this one.
- Krylov–Bogolyubov theorem
- Ergodic decomposition
- Cartan–Hadamard theorem
- Determinacy
- Analytic set
- Preissmann's theorem
- Projective determinacy
- Prokhorov's theorem
- Standard Borel space
- Variational principle for topological entropy
- Unique ergodicity
- Ekeland's variational principle
- Caristi fixed-point theorem
- Projective hierarchy
- Baire space of sequences
- Hilbert manifold
- Hilbert space
- Alexandrov space
- Hopf–Rinow theorem
- Iterated function system
- Polish space
- Axiom of determinacy
Further reading
- Web https://en.wikipedia.org/wiki/Complete_metric_space, lead section
About this page
| Tag | 0BY52JW6NK |
|---|---|
| URI | m2://0BY52JW6NK |
| Aliases | complete-space |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54E50 |
| Specializes | Metric space |
| 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)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- Prokhorov's theorem
- Standard Borel space
- Ekeland's variational principle
- Caristi fixed-point theorem
- Baire space of sequences
- Hilbert space
- Alexandrov space
- Hopf–Rinow theorem
- Iterated function system
- Polish space