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  1. Jul 10, 2008 #1
    Let [tex]{\mathbb I} = {\mathbb R} \setminus {\mathbb Q}[/tex] the set of the irrational numbers of the real line.

    What is the topological dimension of
    [tex]{\mathbb R}^2 \setminus {\mathbb I} \times {\mathbb I}[/tex] ????
  2. jcsd
  3. Jul 11, 2008 #2

    Just discovered, by myself, that it is 1 .


    I just hope that someone can enjoy this result as I do!
    Last edited: Jul 11, 2008
  4. Jul 11, 2008 #3
    Could you explain what is topological dimension please?
  5. Jul 11, 2008 #4

    We say a topological space X has topological dimension m if every covering C of X has a refinementC' in which every point of X occurs in at most m+1 sets in C' , and m is the smallest such integer. Actually, this version of the definition of dimension (called the covering dimension) makes the most sense for compact spaces X.
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