Sigma Algebra

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Hello all,

May someone give me an example of sigma-algebra which is not countably generated?

Apparently such example can only be found in a non-separable space?

Taking [tex]\mathbb R[/tex] as example,

1) Sigma-algebra generated by any subsets of a separable space is countably generated?

2) That in a non-compact space may also be countably generated?

3) That in a compact space is countably generated?

Please kindly address my correctness of the above statements. Thanks very much.

Wayne
 
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