Urysohns

Urysohns is a surname of Russian origin, typically transliterated in English as Urysohn. The plural Urysohns refers to multiple individuals bearing this surname. The name is most often encountered in mathematical and academic contexts due to the contributions of Pavel Samuilovich Urysohn and those associated with his work.

The most prominent bearer of the name is Pavel Samuilovich Urysohn (1898–1924), a Russian mathematician whose work helped establish key foundations of topology. His results led to several theorems and constructions that carry his name, most notably Urysohn's lemma, which concerns extending continuous functions on normal spaces. He is also associated with the concept of the Urysohn universal metric space, a separable complete metric space that is universal for separable metric spaces and homogeneous. Additionally, the Urysohn metrization theorem, which gives conditions under which a topological space is metrizable, is named after him. Although his career was brief, his ideas influenced later developments in topology and metric geometry.

In broader reference, the surname Urysohn appears in various scholarly contexts and genealogies within the Russian and international mathematical communities. Different transliterations may be seen in sources, but Urysohn remains the standard form in most mathematical literature.