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Math Help - One-point compactification

  1. #1
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    One-point compactification

    (I know I'm posting a lot of questions, but I have an exam on Tuesday...)

    Find (and draw) a subspace of R^3 that is homeomorphic to the one-point compactification of X when

    X = (0,1) x (0,1) \ [0,1/2] x [0,1/2]
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  2. #2
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    Quote Originally Posted by claves View Post
    (I know I'm posting a lot of questions, but I have an exam on Tuesday...)

    Find (and draw) a subspace of R^3 that is homeomorphic to the one-point compactification of X when

    X = (0,1) x (0,1) \ [0,1/2] x [0,1/2]
    X is homeomorphic to \mathbb{R}^2. One-point compactification \mathbb{R}_\infty^{2} of \mathbb{R}^2 is homeomorphic to two-dimensional sphere S^2=\{x = (x_1, x_2, x_3) \in \mathbb{R}^3: ||x||=1\}.
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