open set

a subset $\text{[math]}$ is open if for every point $\text{[math]}$ , there exists $\text{[math]}$ such that the open ball $\text{[math]}$ is contained in $\text{[math]}$ .
[cite:@calc_hubbard_2015 definition 1.5.2]

the rectangle
$\text{[math]}$ is open.

a set that is not open is not necessarily closed. an open set owns none of its fence. a closed set owns all of its fence.