Meital Posted September 6, 2005 Share Posted September 6, 2005 Can someone give me an example of a topology, which is not sigma algebra? Link to comment Share on other sites More sharing options...
matt grime Posted September 6, 2005 Share Posted September 6, 2005 A sigma algebra is closed under the operation of complements. Give me a topology (ie a collection of open sets) that is not closed under complements (pretty much most of the ones you can think of, I imagine) Link to comment Share on other sites More sharing options...
Meital Posted September 6, 2005 Author Share Posted September 6, 2005 I see, so we can take the colletion: R ( real numbers), open set (0,2), and the empty set. This is topology since it satisfies all 3 axioms of topology, but not sigma-algebra because we don't have the comp of (0,2) in the collection. Link to comment Share on other sites More sharing options...
matt grime Posted September 6, 2005 Share Posted September 6, 2005 well, that is an odd example to me, but works. R with its usual metric topology was the obvious example. Link to comment Share on other sites More sharing options...
Haroon Stephen Posted June 26, 2018 Share Posted June 26, 2018 On 9/6/2005 at 2:26 AM, Meital said: Can someone give me an example of a topology, which is not sigma algebra? For a set S={1,2,3} consider T={{ }, {1,2}, {2}, {2,3}, S}. T is a topology but not a sigma-algebra. Link to comment Share on other sites More sharing options...
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