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Urysohn graduated in 1919 and became an assistant professor at the University of Moscow in 1921.
Urysohn's first work was concerned with integral equations but he soon turned to topology publishing his first publication on this topic in 1922. His reports to the Mathematical Society of Göttingen in 1923 interested Hilbert.
Urysohn collaborated with Aleksandrov and most of his important work was only published after his death at a very young age. His main results are the introduction and investigation of a class of normal surfaces, metrization theorems and the theory of dimensionality. He is remembered particuarly for 'Urysohn's lemma' which proves the existence of a certain continuous function taking values 0 and 1 on particular closed subsets.
In the summer of 1924 he set off on a European trip through Germany, Holland and France. He met Brouwer and Hausdorff who were impressed with Urysohn's results. After this he continued his holiday to Brittany where he drowned off the coast.
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