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Sigma Algebra

  1. May 11, 2010 #1
    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.

    Last edited: May 11, 2010
  2. jcsd
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