Alexander Arhangelskii

[1] In 1959, in the thesis he wrote for his specialist degree, he introduced the concept of a network of a topological space.

Now considered a fundamental topological notion, a network is a collection of subsets that is similar to a basis, without the requirement that the sets be open.

[1] He received his Candidate of Sciences degree (equivalent to a Ph.D.) in 1962 from the Steklov Institute of Mathematics, supervised by Alexandrov.

Solving a problem posed in 1923 by Alexandrov and Urysohn, he proved that a first-countable, compact Hausdorff space must have a cardinality no greater than the continuum.

Returning under very uncertain conditions, he began to seek academic opportunities in the United States.