Bolzano-Weierstrass theorem
Given any bounded sequence (an) of real numbers,
there exists a convergent subsequence (anj).
More generally, any sequence (an) in a compact subset of a metric space has a convergent subsequence.
| Title | Bolzano-Weierstrass theorem |
|---|---|
| Canonical name | BolzanoWeierstrassTheorem |
| Date of creation | 2013-03-22 12:22:21 |
| Last modified on | 2013-03-22 12:22:21 |
| Owner | yark (2760) |
| Last modified by | yark (2760) |
| Numerical id | 10 |
| Author | yark (2760) |
| Entry type | Theorem |
| Classification | msc 26A06 |
| Classification | msc 40A05 |
| Synonym | Bolzano-Weierstraß theorem |
| Related topic | ConvergentSequence |
| Related topic | SequentiallyCompact |
| Related topic | AlternateStatementOfBolzanoWeierstrassTheorem |