Statements (13)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
normal spaces
|
| gptkbp:category |
separation axiom
|
| gptkbp:field |
gptkb:topology
|
| https://www.w3.org/2000/01/rdf-schema#label |
Urysohn lemma
|
| gptkbp:implies |
normal spaces are Tychonoff
|
| gptkbp:namedAfter |
gptkb:Pavel_Urysohn
|
| gptkbp:relatedTo |
gptkb:Tietze_extension_theorem
|
| gptkbp:sentence |
If X is a normal topological space and A, B are disjoint closed subsets of X, then there exists a continuous function f: X → [0,1] such that f(A)=0 and f(B)=1.
|
| gptkbp:usedIn |
proof of Urysohn metrization theorem
|
| gptkbp:yearProposed |
1925
|
| gptkbp:bfsParent |
gptkb:Tychonoff_space
|
| gptkbp:bfsLayer |
7
|