Vadim Arsen'evič Efremovič (Вади́м Арсе́ньевич Ефре́мович: c. 1903 - May 1, 1989) was a Soviet mathematician. (The spelling "Efremovic" is often seen.)

Efremovič was a member of the Moscow Topological School, and specialized in the geometric aspects of general topology

General topology

In mathematics, general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them...

. He introduced the notion of proximity space

Proximity space

In topology, a proximity space is an axiomatization of notions of "nearness" that hold set-to-set, as opposed to the better known point-to-set notions that characterize topological spaces....

s at the First International Topological Conference in Moscow in 1934. 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.

Efremovič also introduced the notion of "volume invariants" for "equimorphisms" (that is, uniformly bicontinuous) on metric space

Metric space

In mathematics, a metric space is a set where a notion of distance between elements of the set is defined.The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space...

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

Manifold

In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....

s and hyperbolic geometry

Hyperbolic geometry

In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...

.