wayneckm
May11-10, 06:51 PM
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 \mathbb R 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
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 \mathbb R 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