On the Bisectors of Weakly Separable Sets

Abstract. A bisector of two sets is the set of points equidistant to them. Bisectors arise naturally in several areas of computational geometry. We show that bisectors of weakly linearly separable sets in E d share many properties with separating lines. Among these, the bisector of a restricted class of linearly separated sets is a homeomorphic image of the linear separator. We also give necessary and sufficient conditions for the existence of a particular continuous map from a portion of any linear separator to the bisector