= Punctured ball
{title2=$B_r(p)\setminus\{p\}$}
A punctured ball is an <open ball> with its centre removed. In the <real line> it has two <connected components>. In <Euclidean space> of dimension $n\geq2$ it is <path-connected>: for any two points, choose a third point inside the ball outside the two <lines> through the centre and those points. Such a point exists since two <lines> do not cover an <open ball> in dimension at least two. The two <line segments> joining through that point stay inside the ball, which is a <convex set>, and avoid its centre. They form a <continuous path>.
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