Points and lines in metric spaces

Václav Chvátal

Concordia University, Montreal; Canada Research Chair in Discrete Mathematics

Abstract

The notion of lines in a Euclidean spaces can be generalized to a definition of lines in metric spaces in at least two distinct ways. The classical Sylvester-Gallai theorem of Euclidean geometry has been generalized to all metric spaces with one of the two definitions of lines; its corollary, customarily and not quite correctly referred to as a De Bruijn-Erdos theorem, has been conjectured to allow a generalization to all metric spaces with the other definition of lines.