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Math Help - subsets problem in metric spaces

  1. #1
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    subsets problem in metric spaces

    let X be a metric space and A an open subset of X
    Prove that A ∩ B ⊂ (A∩B)

    My approach:
    let x∈A ∩ B
    Then x∈A and x∈B
    nbhd(x) intersects A and B for all ε >0
    so x∈ AB
    but (A∩B)AB
    Did I do anything wrong or miss something?
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: subsets problem in metric spaces

    **I was Wrong
    Last edited by jakncoke; November 26th 2012 at 10:15 PM.
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