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Math Help - Show that unit sphere in R3 is closed

  1. #1
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    Show that the unit sphere in R3 is closed

    EDIT: I've posted this in the wrong part of the forum, please ignore this question.

    Hi, my question is:

    Show that the unit sphere with center 0 in R3, namely the set S2 :={x in R3 : (x1)^2+(x2)^2+(x3)^2=1} is closed in R3.

    What I've done so far is say that to prove it's closed, I need to show that the complement of S2, X`S2, is open, so:

    X`S2 :={x in R3 : (x1)^2+(x2)^2+(x3)^2 is not equal to 1}. I then stated the definition of an open set:

    X`S2 is open if for all x in S2 there exists r>0 such that B(x, r) is a subset of S2, B(x, r)={y : d(x, y)<r}.

    What I'm stuck on in this question is the choice of r, and how to show that, for any y in B(x,r), y is in S2.

    Any help would be appreciated
    Last edited by sakuraxkisu; October 23rd 2013 at 01:08 PM.
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  2. #2
    Junior Member
    Joined
    Mar 2011
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    Re: Show that unit sphere in R3 is closed

    Oh dear, sorry I didn't the see the pre-university part, please ignore this post! I'll post it in the university section now.
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