Pavel Samuilovich Urysohn was a Soviet mathematician who is best known for his contributions to the theory of topological dimension, and for developing Urysohn's metrization theorem and Urysohn's lemma, both of which are fundamental results in topology. He also constructed what is now called the Urysohn universal space and his name is also commemorated in the terms Fréchet–Urysohn space, Menger–Urysohn dimension and Urysohn integral equation. He and Pavel Alexandrov formulated the modern definition of compactness in 1923.