Vadim Arsenyevich Yefremovich (or Efremovich) (russian: Вади́м Арсе́ньевич Ефре́мович; 16 October 1903 – 1 May 1989) was a
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...
mathematician.
Yefremovich was a member of the
Moscow Topological School, and specialized in the geometric aspects of
general topology
In mathematics, general 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 differential topology, geomet ...
. 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 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 the mathematical field of topology, a homeomorphism, topological isomorphism, or bicontinuous function is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorph ...
) on
metric space
In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general settin ...
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 Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:
:For any given line ''R'' and point ''P'' ...
.
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