= Voronoi cell
{c}
{title2=$V_j=\{x:\|x-m_j\|\le\|x-m_\ell\|\text{ for all }\ell\}$}
For centres $m_1,\ldots,m_r$ in <Euclidean space>, the <Voronoi cell> of $m_j$ is the set of points at least as close to $m_j$ as to every other centre. Shared boundaries consist of points tied between nearest centres; assigning each such point to one centre makes the cells a <partition of a set>.
On the real line with distinct ordered centres, the <Voronoi cells> are <intervals>, with boundaries at the midpoints of adjacent centres. This makes nearest-centre clusters contiguous blocks of sorted observations in <k-means clustering>.
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