Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
spaces of continuous functions
|
| gptkbp:category |
compactness theorems
|
| gptkbp:concerns |
compactness
function spaces equicontinuity |
| gptkbp:field |
mathematical analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Arzelà–Ascoli theorem
|
| gptkbp:namedAfter |
gptkb:Cesare_Arzelà
gptkb:Giulio_Ascoli |
| gptkbp:publishedIn |
19th century
|
| gptkbp:relatedTo |
gptkb:Banach–Alaoglu_theorem
gptkb:Heine–Borel_theorem |
| gptkbp:state |
A subset of C(K) is relatively compact if and only if it is equicontinuous, pointwise relatively compact, and bounded.
|
| gptkbp:usedIn |
gptkb:topology
functional analysis real analysis |
| gptkbp:bfsParent |
gptkb:Montel's_theorem
gptkb:Real_Analysis |
| gptkbp:bfsLayer |
7
|