Alexander Arhangelskii

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Alexander Arhangelskii
Born13 March 1938
Moscow, Soviet Union
Alma materMoscow State University
Known forGeneral topology
Scientific career
FieldsMathematics
InstitutionsMoscow State University, Ohio University
Doctoral advisorPavel Alexandrov
Doctoral studentsMitrofan Cioban

Alexander Vladimirovich Arhangelskii (

metrizability theory and generalized metric spaces, cardinal functions, topological function spaces and other topological groups, and special classes of topological maps. After a long and distinguished career at Moscow State University, he moved to the United States in the 1990s. In 1993 he joined the faculty of Ohio University
, from which he retired in 2011.

Biography

Arhangelskii was the son of Vladimir Alexandrovich Arhangelskii and Maria Pavlova Radimova, who divorced by the time he was four years old. He was raised in Moscow by his father. He was also close to his uncle, childless aircraft designer

Alexander Arkhangelsky. In 1954, Arhangelskii entered Moscow State University, where he became a student of Pavel Alexandrov. At the end of his first year, Arhangelskii told Alexandrov that he wanted to specialize in topology.[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.[2] Also in 1959 he married Olga Constantinovna.[1]

He received his Candidate of Sciences degree (equivalent to a Ph.D.) in 1962 from the Steklov Institute of Mathematics, supervised by Alexandrov.[3] He was granted the Doctor of Sciences degree in 1966.

It was in 1969 that Arhangelskii published what is considered his most significant mathematical result. 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
. In fact, his theorem is much more general, giving an upper bound on the cardinality of any Hausdorff space in terms of two cardinal functions. Specifically, he showed that for any Hausdorff space X,

where χ(X) is the character, and L(X) is the Lindelöf number. Chris Good referred to Arhangelskii's theorem as an "impressive result", and "a model for many other results in the field."[4] Richard Hodel has called it "perhaps the most exciting and dramatic of the difficult inequalities",[5] a "beautiful inequality", and "the most important inequality in cardinal invariants."[6]

In 1970 Arhangelskii became a full professor, still at Moscow State University. He spent 1972–75 on leave in

University of Islamabad under a UNESCO program.[1]

Arhangelskii took advantage of the few available opportunities to travel to mathematical conferences outside of the Soviet Union.

Distinguished Professor Award in 2003.[8]

Arhangelskii was one of the founders of the journal

Topology and its Applications, and volume 153 issue 13, July 2006, was a special issue, with most of the papers based on talks given at a special conference held at Brooklyn College
30 June–3 July 2003 in honor of his 65th birthday.

Selected publications

Books

Papers

References

  1. ^
    ISSN 1499-9226. Archived from the original on 13 February 2017. Retrieved 18 June 2012. (reprinted from the Summer 1993 issue of The Idler
    )
  2. ISBN 978-0444503558
    .
  3. ^ Alexander V. Arhangelskii at the Mathematics Genealogy Project
  4. ISBN 978-0444503558
    .
  5. ISBN 0-444-86580-2
    .
  6. ISSN 0166-8641
    . Retrieved 23 January 2012.
  7. ^ Yetter, David (1993). "Moscow, money, and mathematics: An interview with Alexander Arhangel'skii" (PDF). Friends of Mathematics Newsletter. Kansas State University Department of Mathematics. Archived from the original (PDF) on 2013-10-04. Retrieved 18 June 2012.
  8. ^ "Two Ohio University faculty members named Distinguished Professor". Outlook. Ohio University. 2 October 2003. Archived from the original on 6 March 2016. Retrieved 18 June 2012.

External links

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