Notation regarding Balls

Question

What is meant by the notation :

$y \in \partial B_\epsilon (x_o)$

Where B is a Ball centred at $x_0$ with radius $\epsilon$

Answer 1

It is the boundary of the ball.

Answer 2

When you are in a normed space, with norm $\|\cdot \|$, then $$\partial B_\epsilon(x_0)=:\{x: \|x-x_0\|=\epsilon\},$$ the boundary of $B_\epsilon(x_0)$. More generally the notation $\partial E$, with $E$ a set, denotes its boundary.