Two distinct theorems are referred to as "the de Bruijn-Erdős theorem." One of them (de Bruijn and Erdős 1951) concerns the chromatic number of infinite
graphs; the other (de Bruijn and Erdős 1948) states that every noncollinear
set of
points in the plane determines at least distinct lines.
Chen and Chvátal (2006) have partially generalized the (second) de Bruijn-Erdős
theorem in the framework of metric spaces.
Chen, X. and Chvátal, V. "Problems Related to a de Bruijn-Erdős Theorem." Submitted to Elsevier Preprint, Apr.
18, 2006.de Bruijn, N. G. and Erdős, P. "On a Combinatorial
Problem." Indag. Math.10, 421-423, 1948.de Bruijn,
N. G. and Erdős, P. "A Colour Problem for Infinite Graphs and a Problem
in the Theory of Relations." Indag. Math.13, 369-373, 1951.
points in the plane determines at least 
distinct lines.
