# Math Help - Is this set closed and bounded?

1. ## 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

2. Originally Posted by Siknature
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