Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Euclidean_space
real numbers |
| gptkbp:category |
theorems in analysis
theorems in topology |
| gptkbp:field |
gptkb:topology
mathematical analysis |
| gptkbp:firstPublished |
19th century
|
| gptkbp:generalizes |
sequential compactness in metric spaces
|
| https://www.w3.org/2000/01/rdf-schema#label |
Bolzano–Weierstrass theorem
|
| gptkbp:implies |
every bounded sequence in ℝ has a convergent subsequence
|
| gptkbp:namedAfter |
gptkb:Karl_Weierstrass
gptkb:Bernard_Bolzano |
| gptkbp:relatedTo |
gptkb:Heine–Borel_theorem
compactness sequential compactness |
| gptkbp:sentence |
Every bounded sequence in ℝⁿ has a convergent subsequence.
|
| gptkbp:usedIn |
real analysis
metric spaces |
| gptkbp:bfsParent |
gptkb:Bernard_Bolzano
|
| gptkbp:bfsLayer |
5
|