Denis Higgs
| Denis A. Higgs | |
|---|---|
| Born |
6 May 1932 England |
| Died |
25 February 2011 (aged 78) Toronto Canada |
| Nationality | British |
| Fields | Mathematics |
| Institutions | University of the Witwatersrand, University of Cambridge, University of Waterloo |
| Alma mater | University of Cambridge, University of the Witwatersrand |
| Thesis | Matroids on Complete Boolean Algebras (1970) |
| Doctoral advisor | Gert Sabidussi |
| Notable students | Philip Scott, Peter Schotch |
| Known for |
Category theory Combinatorics Universal algebra |
Denis A. Higgs (6 May 1932 – February 25, 2011) was a British mathematician, Doctor of Mathematics, and professor of mathematics who specialised in combinatorics, universal algebra, and category theory. He wrote one of the most influential papers in category theory entitled A category approach to boolean valued set theory, which introduced many students to topos theory.[1] He was a member of the National Committee of Liberation and was an outspoken critic against the apartheid in South Africa.
Life
He earned degrees from Cambridge University, St John's College, in England and University of the Witwatersrand in South Africa,
In 1962, he became a member of the National Committee of Liberation, a movement whose main objective was to dismantle the apartheid in South Africa.[2]
On 28 August 1964, he was kidnapped from his home in Lusaka, Zambia. Then South Africa's Justice Minister John Vorster, who later became Prime Minister, denied any involvement by either the South African government or the police.[3]
On 1 September, an unidentified man who claimed to be part of British Protectorates, called the Rand Daily Mail newspaper and gave specific details of Denis Higgs's whereabouts. And on 2 September, police authorities found him. He was blindfolded and bound in a van over by the Zoo Park area.[3]
On 6 September 1964, he fled to London, accompanied by his family. He later stated that he feared for his safety and that of his family, since a day before his departure, the South African government had begun proceedings of extradition for his alleged participation in the explosion at the Johannesburg Railway Station.[2]
Career
He emigrated to Canada in 1966, and held a position as a professor of Pure Mathematics at the University of Waterloo, where he wrote one of the most influential papers in category theory entitled A category approach to boolean valued set theory, which introduced many students to topos theory.[1]
In 1973, he generalised the Rasiowa-Sikorski Boolean models to the case of category theory.[4]
His academic papers have been published in Algebra Universalis, in the Journal of Pure and Applied Algebra, in the Journal of the Australian Mathematical Society, in the Journal of the London Mathematical Society, and in the Mathematics of Computation journals, among others.
He died on 25 February 2011.[5]
Academic publications
- Denis Higgs (1989). "Nuclearity in the category of complete semilattices". Journal of Pure and Applied Algebra. 57 (1): 67–78. doi:10.1016/0022-4049(89)90028-5.
- Don Brunker; Denis Higgs (1989). "Constructions of Σ-groups, relatively free Σ-groups". Journal of the Australian Mathematical Society. 46 (01). doi:10.1017/S1446788700030354.
- Denis Higgs (1989). "Remarks on duality for ?-groups: Banach and Hilbert spaces". Advances in Mathematics. 76 (2): 230–244. doi:10.1016/0001-8708(89)90052-2.
- Denis Higgs (1988). "Σ-Groups as Convergence Groups". Mathematische Nachrichten. 137 (1): 101–112. doi:10.1002/mana.19881370110.
- Denis Higgs (1986). "Lattices of crosscuts". Algebra Universalis. 23 (1): 10–18. doi:10.1007/BF01190905.
- Denis Higgs (1985). "A companion to Grillet's Theorem on maximal chains and antichains". A Journal on The Theory of Ordered Sets and Its Applications. 1 (4): 371–375. doi:10.1007/BF00582742.
- J. E. Baumgartner; D. Higgs (1984). "Cross-cuts in the power set of an infinite set". A Journal on The Theory of Ordered Sets and Its Applications. 1 (2): 139–145. doi:10.1007/BF00565649.
- D. Handelman; D. Higgs; J. Lawrence (1980). "Directed Abelian Groups, Countably Continuous Rings, and Rickart C*-Algebras". Journal of the London Mathematical Society. s2-21 (2): 193–202. doi:10.1112/jlms/s2-21.2.193.
- D. Higgs (1978). "A Universal Characterization of [0, ∞]". Indagationes Mathematicae (proceedings). 81 (1): 448–455. doi:10.1016/S1385-7258(78)80035-3.
- John E. Blackburn; Henry H. Crapo; Denis A. Higgs (1973). "A Catalogue of Combinatorial Geometries". Mathematics of Computation. 27 (121). doi:10.2307/2005258.
- John E. Blackburn; Henry H. Crapo; Denis A. Higgs (1973). "A catalogue of combinatorial geometries". Mathematics of Computation. 27 (121): 155–155. doi:10.1090/S0025-5718-1973-0419270-0.
- Denis Higgs (1971). "Remarks on residually small varieties". Algebra Universalis. 1 (1): 383–385. doi:10.1007/BF02944997.
- Denis Higgs (1971). "Lattices isomorphic to their ideal lattices". Algebra Universalis. 1 (1): 71–72. doi:10.1007/BF02944957.
- Denis Higgs (1970). "Boolean-valued equivalence relations and complete extensions of complete boolean algebras". Bulletin of the Australian Mathematical Society. 3 (01). doi:10.1017/S0004972700045652.
- Denis Higgs. Interpolation antichains in lattices. doi:10.1007/BFb0098461.
References
- 1 2 Scott, Phil (7 March 2011). "Denis Higgs". Mount Allison University. Retrieved 14 December 2012.
- 1 2 South African Democracy Education Trust (2004). The Road to Democracy in South Africa (1960–1970). The Road to Democracy in South Africa. Zebra Press. ISBN 9781868729067. LCCN 2004448218.
- 1 2 "Kidnapped Teacher Goes Back to Rhodesia". The Sydney Morning Herald. 3 September 1964. Retrieved 7 December 2012.
- ↑ Mostowski, A.; Ehrenfeucht, A.; Marek, V.W.; Srebrny, M. (2008). Andrzej Mostowski and Foundational Studies. Ios Press Inc. ISBN 9781586037826. LCCN 2007939570.
- ↑ "Notices of the AMS" (PDF). Notices of the American Mathematical Society. American Mathematical Society. 58 (5): 731. 2011.