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Homework Help: Embeding function

  1. Nov 28, 2008 #1
    1. The problem statement, all variables and given/known data

    X is a space with the property that {X\{m}:m[tex]\in[/tex]X}[tex]\subseteq\tau(X)[/tex].
    2={0,1}.
    Prove that X can be embeded in [tex]\prod_{\tau(X)}2[/tex].

    2. Relevant equations

    [tex]\tau(X)=\{\emptyset,\{0\},\{0,1\}\}[/tex].

    3. The attempt at a solution
    I have a few simple questions.
    Why is the product indexing over the topology on X? What does[tex]\prod_{\tau(X)}2[/tex] look like? What does the space X look like?
    Any insight in pointing me in the right direction would be helpful since I do not have many examples of embeded functions.
     
  2. jcsd
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