Is A open or closed? Is it a bounded set? Verify if the given set $A$ it's open or closed. Also verify if it's bounded.
a) $A = \{ (x,y) \in \mathbb{R}^2 \mid x^2 + y^2 < 1\}$
I just want the method for verify this things in case of this example, because I have items a,b,c,d,e to do. The other sets are usually points of $\mathbb{R}^2$.

we can paremeterize it $x=rcos\theta ,y=rsin\theta $
$A = \{ (x,y) \in \mathbb{R}^2 \mid x^2 + y^2 < 1\}$
then we can Write $r^2\lt1 $
no matter how small $\epsilon $ ball you take in $A$ it will always be contained in $A$ hence the Set A is an open set.
