Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Euclidean_space
real numbers |
| gptkbp:category |
theorems in analysis
|
| 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 infinite subset of ℝⁿ has a limit point
|
| gptkbp:namedAfter |
gptkb:Karl_Weierstrass
gptkb:Bernard_Bolzano |
| gptkbp:relatedTo |
gptkb:Heine-Borel_theorem
compactness sequential compactness |
| gptkbp:state |
every bounded sequence in ℝⁿ has a convergent subsequence
|
| gptkbp:usedIn |
real analysis
metric spaces |
| gptkbp:bfsParent |
gptkb:Real_Analysis
|
| gptkbp:bfsLayer |
7
|