The fathers of dimension
pp. 395-434
in: , L. E. J. Brouwer – topologist, intuitionist, philosopher, Berlin, Springer, 2013Abstract
In this chapter we find a complete return to topology, to be precise, to dimension theory. In 1923 Brouwer attended the Marburg meeting of the German Math Society, at that same meeting there was a young Russian topologist, Urysohn, who had given a definition of dimension unaware of the fact that Brouwer had already done so. When his attention was called to this fact he checked Brouwer's 1913 paper and found a mistake. He informed Brouwer and the latter immediately set out to check his old paper. Indeed there was a erroneous detail in the definition. The two corresponded about the matter and eventually agreed that Brouwer's mistake was a slip of the pen (born out by solid evidence). Almost at the same time Menger had studied the topic and given his own definition of dimension. In 1924 Urysohn and Alexandrov visited Germany, went on to see Brouwer and then went on to France. Urysohn died when swimming in rough weather at the coast of Brittany. Alexandrov and Brouwer were inconsolable, they decided to edit Urysohn's scientific estate.