# Math Help - Open or Closed?

1. ## Open or Closed?

Let

$A=\left\{ (a,b)\in\mathbb{R}^{2}:\:0\leq a<3,\:0\leq b\leq5\right\}$

Determine whether A is open, closed or neither. What is the closure, interior and boundary of A?

I was under the impression that the set is neither open nor closed, but am struggling to prove this.

2. ## Re: Open or Closed?

Originally Posted by Cairo
Let
$A=\left\{ (a,b)\in\mathbb{R}^{2}:\:0\leq a<3,\:0\leq b\leq5\right\}$
Determine whether A is open, closed or neither. What is the closure, interior and boundary of A?
True or false: $(3,5)\in A~?$

Can you show that $(3,5)\in\beta(A)$, the boundary of A.

3. ## Re: Open or Closed?

you might want to consider the following subsets of $\mathbb{R}^2$:

{0}x[0,5], {3}x[0,5], [0,3]x{0}, [0,3]x{5}.

which of these are entirely in A?