Difference between revisions of "Urysohn lemma"
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The '''Urysohn lemma''' states: | The '''Urysohn lemma''' states: | ||
<blockquote> | <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 | + | 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> | </blockquote> | ||
| + | The converse of the Urysohn lemma also holds. | ||
[[category: Topology]] | [[category: Topology]] | ||
Revision as of 18:37, April 6, 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.