A bisector of two sets is the set of points equidistant form them. Bisectors arise naturally in several areas of computational geometry. We show that bisectors of weakly linearly separable sets in E d have many properties of interest. 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. © 1991 Springer-Verlag New York Inc.