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Show that the set S={(x,y) | xy=1, x>0 } is closed in R^2
I came up with a way to show that S is homeomorphic to x axis by some projections, therefore closed. but my class has only talked about open, closed set in a metric space so far. I don't know how to prove it by showing that the complement is open. Since constructing an open ball for every point outside the curve has been mathematically daunting. ( always bumped into some almost uncalculatable polynomial expressions). Help.
Last edited by Dragonshade (2011-01-21 11:43:34)
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