Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
compact Hausdorff spaces
algebras of functions |
| gptkbp:concerns |
approximation of functions
|
| gptkbp:field |
mathematical analysis
|
| gptkbp:generalizes |
gptkb:Weierstrass_approximation_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Stone-Weierstrass theorem
|
| gptkbp:namedAfter |
gptkb:Karl_Weierstrass
gptkb:Marshall_H._Stone |
| gptkbp:relatedTo |
gptkb:C*-algebra
continuous functions uniform convergence |
| gptkbp:state |
Any subalgebra of C(X) that separates points and contains the constant functions is dense in C(X) with the uniform norm, where X is a compact Hausdorff space.
|
| gptkbp:usedIn |
gptkb:topology
functional analysis approximation theory |
| gptkbp:yearProved |
1937
|
| gptkbp:bfsParent |
gptkb:Real_Analysis
|
| gptkbp:bfsLayer |
7
|