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Clifford Hugh Dowker

March 11, 2023

Clifford Hugh Dowker (/ˈdaʊkər/; March 2, 1912 – October 14, 1982) was a topologist known for his work in point-set topology and also for his contributions in category theory, sheaf theory and knot theory.

Biography

Clifford Hugh Dowker grew up on a small farm in Western Ontario, Canada. He excelled in mathematics and was paid to teach his math teacher math at his secondary school. He was awarded a scholarship at Western Ontario University, where he got his B.S. in 1933. He wanted to pursue a career as a teacher, but he was persuaded to continue with his education because of his extraordinary mathematical talent. He earned his M.A. from the University of Toronto in 1936 and his Ph.D. from Princeton University in 1938. His dissertation Mapping theorems in non-compact spaces was written under the supervision of Solomon Lefschetz and was published (with additions) in 1947 in the American Journal of Mathematics.[1][2] After earning his doctorate, Dowker became an instructor at the Western Ontario University for a year. The next year, he worked as an assistant back at Princeton under John von Neumann. During World War II, he worked for the U.S. Air Force, calculating the trajectories of projectiles. He married Yael Naim in 1944. After the war, he was appointed associate professor at the Tufts University. Because of Senator Joseph McCarthy's red scare, he decided to take his family to England shortly thereafter, where he was appointed Reader in applied mathematics at Birkbeck College in 1951. In 1962 he was granted a personal chair, until he retired in 1979. The last years of his life were marked by a long illness, yet he continued working, developing Dowker notation in the weeks before his death.[3][4]

Work

Dowker showed that Čech and Vietoris homology groups coincide, as do the Čech cohomology and Alexander cohomology groups.[5] Along with Morwen Thistlethwaite, he developed Dowker notation, a simple way of describing knots, suitable for computers.[6]

His most highly cited article is his 1951 paper in which he introduced the concept of countably paracompact spaces.[7] Dowker conjectured that so-called Dowker spaces could not exist, a conjecture ultimately proven false[8] in a famous 1971 paper by Mary Ellen Rudin.[1][9]

See also

References

  1. ^ a b James, I. M.; Kronheimer, Erwin Heinz, eds. (31 January 1985). "Obituary. Clifford Hugh Dowker". Aspects of Topology: In Memory of Hugh Dowker 1912-1982. pp. xi≠xvii. ISBN 9780521278157.
  2. ^ Dowker, C. H. (1947). "Mapping Theorems for Non-Compact Spaces". American Journal of Mathematics. 69 (2): 200–242. doi:10.2307/2371848. JSTOR 2371848.
  3. ^ Dowker biography
  4. ^ Times obituary
  5. ^ http://www.cmi.ac.in/~strivedi/MScThesis.pdf[bare URL PDF]
  6. ^ Weisstein, Eric W. "Dowker Notation." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DowkerNotation.html
  7. ^ Dowker, C. H. (1951). "On Countably Paracompact Spaces". Canadian Journal of Mathematics. 3: 219–224. doi:10.4153/CJM-1951-026-2. S2CID 125051945.
  8. ^ Kojman, Menachem; Shelah, Saharon (1995). "A ZFC Dowker space in ℵω+1: An application of PCF theory to topology". arXiv:math/9512202.
  9. ^ Rudin, Mary Ellen (1971). "A normal space X for which X × I is not normal". Fundam. Math. 73 (2): 179–186. doi:10.4064/fm-73-2-179-186. Zbl 0224.54019.

External links

March 11, 2023
clifford, hugh, dowker, march, 1912, october, 1982, topologist, known, work, point, topology, also, contributions, category, theory, sheaf, theory, knot, theory, contents, biography, work, also, references, external, linksbiography, edit, grew, small, farm, we. Clifford Hugh Dowker ˈ d aʊ k er March 2 1912 October 14 1982 was a topologist known for his work in point set topology and also for his contributions in category theory sheaf theory and knot theory Contents 1 Biography 2 Work 3 See also 4 References 5 External linksBiography EditClifford Hugh Dowker grew up on a small farm in Western Ontario Canada He excelled in mathematics and was paid to teach his math teacher math at his secondary school He was awarded a scholarship at Western Ontario University where he got his B S in 1933 He wanted to pursue a career as a teacher but he was persuaded to continue with his education because of his extraordinary mathematical talent He earned his M A from the University of Toronto in 1936 and his Ph D from Princeton University in 1938 His dissertation Mapping theorems in non compact spaces was written under the supervision of Solomon Lefschetz and was published with additions in 1947 in the American Journal of Mathematics 1 2 After earning his doctorate Dowker became an instructor at the Western Ontario University for a year The next year he worked as an assistant back at Princeton under John von Neumann During World War II he worked for the U S Air Force calculating the trajectories of projectiles He married Yael Naim in 1944 After the war he was appointed associate professor at the Tufts University Because of Senator Joseph McCarthy s red scare he decided to take his family to England shortly thereafter where he was appointed Reader in applied mathematics at Birkbeck College in 1951 In 1962 he was granted a personal chair until he retired in 1979 The last years of his life were marked by a long illness yet he continued working developing Dowker notation in the weeks before his death 3 4 Work EditDowker showed that Cech and Vietoris homology groups coincide as do the Cech cohomology and Alexander cohomology groups 5 Along with Morwen Thistlethwaite he developed Dowker notation a simple way of describing knots suitable for computers 6 His most highly cited article is his 1951 paper in which he introduced the concept of countably paracompact spaces 7 Dowker conjectured that so called Dowker spaces could not exist a conjecture ultimately proven false 8 in a famous 1971 paper by Mary Ellen Rudin 1 9 See also EditDowker notation Dowker space Cech cohomology Morwen Thistlethwaite Sheaf theoryReferences Edit a b James I M Kronheimer Erwin Heinz eds 31 January 1985 Obituary Clifford Hugh Dowker Aspects of Topology In Memory of Hugh Dowker 1912 1982 pp xi xvii ISBN 9780521278157 Dowker C H 1947 Mapping Theorems for Non Compact Spaces American Journal of Mathematics 69 2 200 242 doi 10 2307 2371848 JSTOR 2371848 Dowker biography Times obituary http www cmi ac in strivedi MScThesis pdf bare URL PDF Weisstein Eric W Dowker Notation From MathWorld A Wolfram Web Resource http mathworld wolfram com DowkerNotation html Dowker C H 1951 On Countably Paracompact Spaces Canadian Journal of Mathematics 3 219 224 doi 10 4153 CJM 1951 026 2 S2CID 125051945 Kojman Menachem Shelah Saharon 1995 A ZFC Dowker space in ℵw 1 An application of PCF theory to topology arXiv math 9512202 Rudin Mary Ellen 1971 A normal space X for which X I is not normal Fundam Math 73 2 179 186 doi 10 4064 fm 73 2 179 186 Zbl 0224 54019 External links EditO Connor John J Robertson Edmund F Clifford Hugh Dowker MacTutor History of Mathematics archive University of St Andrews Clifford Hugh Dowker at the Mathematics Genealogy Project Retrieved from https en wikipedia org w index php title Clifford Hugh Dowker amp oldid 1113890162, wikipedia, wiki, book, books, library,

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