The History of Barbilian's Metrization Procedure

Barbilian spaces are metric spaces with a metric induced by a special procedure of metrization which is inspired by the study of the models of non-Euclidean geometry. In the present material we discuss the history of Barbilian spaces and the evolution of the theory. We point out that some of the current references to the work done in Barbilian spaces refer to Barbilian's contribution from 1934, while his construction has been largely extended in four works published in Romanian in 1959-1962.