Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
arbitrary products of compact spaces
|
| gptkbp:category |
gptkb:mathematics
|
| gptkbp:equivalentTo |
axiom of choice
|
| gptkbp:field |
gptkb:topology
|
| gptkbp:firstPublished |
1930
|
| gptkbp:generalizes |
finite product of compact spaces is compact
|
| https://www.w3.org/2000/01/rdf-schema#label |
Tychonoff's theorem
|
| gptkbp:importantFor |
fundamental result in general topology
|
| gptkbp:namedAfter |
gptkb:Andrey_Tychonoff
|
| gptkbp:proofRequires |
axiom of choice
|
| gptkbp:relatedTo |
gptkb:Urysohn's_lemma
Hausdorff space compactness product topology |
| gptkbp:state |
The product of any collection of compact topological spaces is compact in the product topology.
|
| gptkbp:usedIn |
gptkb:set_theory
gptkb:topology functional analysis |
| gptkbp:bfsParent |
gptkb:Axiom_of_Choice
gptkb:Axiom_of_choice |
| gptkbp:bfsLayer |
5
|