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Is there an example of a sigma algebra that is not a topology? If this is not the case, is it possible to prove that all sigma algebras are topologies?

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    The Borel sets in $[0,1]$, obviously. It contains all points but not all subsets.2011-07-13
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    @Claudia: Didn't you pose exactly the same question here yesterday? Maybe I'm going mad...2011-07-13
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    @Stefan: I had the same déjà-vu, [don't worry about your mental health](http://mathoverflow.net/questions/70137/) :) I see only now that Joel made more or less the same point as I did in a comment2011-07-13
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    I do not recall topologies being $\sigma$-algebras at all... They are not usually closed under complements nor countable intersections.2011-07-13
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    @Asaf: The question is the other way around :)2011-07-13
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    See also http://mathoverflow.net/questions/70137/sigma-algebra-that-is-not-a-topology/70152#70152 same question and basically the same answer.2011-07-13
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    Yes I made the same question yesterday, and the answers of today are helping me a lot. Sorry if I bothered you. I will not do it again. Claudia2011-07-13
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    Dear Claudia, because you are using an unregistered acount, the software platform is having difficulty tracking who you are (which resulted in you not being about to comment on the question). I've merged your two accounts for now, and I encourage you to register.2011-07-13

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