open ball

open ball
for any $\text{[math]}$ and any $\text{[math]}$ , the open ball of radius $\text{[math]}$ around $\text{[math]}$ is the subset
$\text{[math]}$ [cite:@calc_hubbard_2015 definition 1.5.1]

note that $\text{[math]}$ must be less than $\text{[math]}$ for the ball to be open; it cannot be $\text{[math]}$ . in dimension 1, a ball is an interval.