Meaning of a symbol

Question

I've seen the symbol "$B_\epsilon(a)$", but I don't know what it means. The context is limits of a subsequence. Here, $\epsilon>0$ is a real number, and the limit of subsequence $a_{n_k}$ is $a$, and $a_{n_k}\in B_\epsilon(a)$ is true for $k$ big enough.

Answer 1

It seems that it is a ball centered in $a$ of radius $\epsilon$: $B_\epsilon(a)=\{x: \|x-a\|<\epsilon\}$.

Answer 2

This is defined to be the “Ball around a with the radius $\epsilon$”: $$B_\epsilon(a):=\{x\in V: d(x, v)<\epsilon\}$$ Where $(V, d)$ is a metric space. $V$ does not necessarily have to be normed.