Closed ball
= Closed ball
{title2=$\overline B(x,r)=\{y:d(x,y)\leq r\}$}
In a <metric space> $(M,d)$, the closed ball centred at $x$ of radius $r\geq0$ is $\{y\in M:d(x,y)\leq r\}$. It is a <closed set>, since the distance to $x$ is a <continuous> <function>. Its boundary need not be the whole corresponding distance sphere in an arbitrary <metric space>.