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Math Help - question about topology in R^2

  1. #1
    bha
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    question about topology in R^2

    hello, i'm looking for example for a closed group in R^2, but its projection on R is not closed. any ideas?
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  2. #2
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    Re: question about topology in R^2

    How about the graph G of the equation y=\ln{x}. It's complement G^C is an open set in \mathbb{R}^2: if you choose a point P not on the curve, it is a distance \epsilon from the curve, so the ball of radius \frac{\epsilon}{2} centered at P is contained in G^C. So G is closed.

    But its projection onto the x-axis is the interval (0,\infty), which is an open interval.

    Is that what you were looking for?

    - Hollywood
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