Definition
20
[0NW] Let \(xβ X, r{\gt}0\) be given; we will indicate with \(B(x,r)\) the ball,
\[ B(x,r){\stackrel{.}{=}}\{ yβ X : d(x,y){\lt} r\} \]
that is also indicated with \(B_ r(x)\); and with
\[ D(x,r){\stackrel{.}{=}}\{ yβ X : d(x,y)β€ r\} \]
the disk, that is also indicated with \({\overline B}_ r(x)\).