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Math Help - show the space is connected

  1. #1
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    show the space is connected

    For n = 1,2,.., let X_n  = \{ \left( {1/n,y} \right) - n \le y \le n\} Show that the subspace R^n  -  \cup _n X_n is connected.
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  2. #2
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    Re: show the space is connected

    Quote Originally Posted by rqeeb View Post
    For n = 1,2,.., let X_n  = \{ \left( {1/n,y} \right) - n \le y \le n\} Show that the subspace R^n  -  \cup _n X_n is connected.
    This has to be a proof by contradiction. Suppose that R^n  -  \cup _n X_n is not connected. Then it is the union of two open disjoint sets U and V.

    Just to get you started, think about the fact that the origin must lie in one of those sets.
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