What does this notation of open sets $B(x,y)$ mean?

Question

I've seen this in various questions like this one here: Prove that the inverse image of an open set is open

I know $(x,y)$ is an open interval, but when someone refers to an open set as $B(x,y)$, what exactly does that mean?

Answer 1

It means an open ball centered at $x$ with radius $y$.

$$B(x,y) = \{ z: \|z-x\| < y \}$$