Vadim Arsenyevich Yefremovich (or Efremovich) (; 16 October 1903 – 1 May 1989) was a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

mathematician. Yefremovich was a member of the Moscow Topological School and specialized in the geometric aspects of

general topology In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differ ...

. He introduced the notion of

proximity space In topology, a proximity space, also called a nearness space, is an axiomatization of the intuitive notion of "nearness" that hold set-to-set, as opposed to the better known point-to-set notion that characterize topological spaces. The concept was ...

s at the

First International Topological Conference The first International Topological Conference was held in Moscow, 4–10 September, 1935. With presentations by topologists from 10 different countries it constituted the first genuinely international meeting devoted to topology in the world hist ...

in Moscow in 1935. He was imprisoned from 1937 to 1944, and did not publish on proximity spaces until 1951, at which point the theory was developed rapidly by Efremovič and associates. Yefremovich also introduced the notion of "volume invariants" for "equimorphisms" (that is, uniformly

bicontinuous In mathematics and more specifically in topology, a homeomorphism ( from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function betw ...

) on

metric space In mathematics, a metric space is a Set (mathematics), set together with a notion of ''distance'' between its Element (mathematics), elements, usually called point (geometry), points. The distance is measured by a function (mathematics), functi ...

s. These have proven to be very important in the study of

manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a N ...

s and

hyperbolic geometry In mathematics, hyperbolic geometry (also called Lobachevskian geometry or János Bolyai, Bolyai–Nikolai Lobachevsky, Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For a ...

References

Bibliography

*Vadim Arsenyevich Yefremovich (obituary), in ''Russian Mathematical Surveys'' 45:6 (1990), pp 137–138. 1903 births 1989 deaths 20th-century Russian mathematicians {{Russia-mathematician-stub