Difference between revisions of "Urysohn lemma"
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| − | < | + | The '''Urysohn lemma''' states: |
| + | <blockquote> | ||
| + | If ''A'', ''B'' are 2 disjoint, closed subsets of a [[normal space]] ''X'', then there exist a [[continuous function]] ''f'' : ''X'' → [0, 1], such that ''f(A)'' = 0 and ''f(B)'' = 1. | ||
| + | </blockquote> | ||
| + | The converse of the Urysohn lemma also holds. | ||
[[category: Topology]] | [[category: Topology]] | ||
Revision as of 23:53, April 30, 2007
The Urysohn lemma states:
If A, B are 2 disjoint, closed subsets of a normal space X, then there exist a continuous function f : X → [0, 1], such that f(A) = 0 and f(B) = 1.
The converse of the Urysohn lemma also holds.