Wikipedia
In discrete geometry, a k-set of a finite point set S in the Euclidean plane is a subset of k elements of S that can be strictly separated from the remaining points by a line. More generally, in Euclidean space of higher dimensions, a k-set of a finite point set is a subset of k elements that can be separated from the remaining points by a hyperplane. In particular, when k = n/2 (where n is the size of S), the line or hyperplane that separates a k-set from the rest of S is a halving line or halving plane.
K-sets are related by projective duality to k-levels in line arrangements; the k-level in an arrangement of n lines in the plane is the curve consisting of the points that lie on one of the lines and have exactly k lines below them. Discrete and computational geometers have also studied levels in arrangements of more general kinds of curves and surfaces.