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Math Help - Is this set closed and bounded?

  1. #1
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    Is this set closed and bounded?

    Is this set closed and bounded?

    A = { (x1,x2) : 0<= x1<=1 , and 0<= x2<=1} in R^2

    I'm trying to show that the set is compact and was thinking i could use the fact that a closed and bounded subset of R^n is compact.

    Or is there a better way to show that this set is compact?

    Thanks
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  2. #2
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    Quote Originally Posted by Siknature View Post
    Is this set closed and bounded?

    A = { (x1,x2) : 0<= x1<=1 , and 0<= x2<=1} in R^2

    I'm trying to show that the set is compact and was thinking i could use the fact that a closed and bounded subset of R^n is compact.

    Or is there a better way to show that this set is compact?

    Thanks

    It is closed and bounded since it is the cartesian product of two closed and bounded sets...
    And yes: I think the best way to prove something's compact in \mathbb{R}^n is showing it is closed and bounded.

    Tonio
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