Towards Glenorchy, Lake Wakatipu, NZ
What's new?
Mar. 2025: 'Monotone convergence theorems equivalent to Markov's Principle'
https://workdrive.zoho.com/file/v10n515966c1edcfb40138eb2eb22c258da5d
The notions of provisional, negative, and apparent convergence to 0 are introduced. It is then shown that Markov's principle is equivalent, in Bishop-
style constructive mathematics, to the statement `every decreasing sequence of real numbers provisionally convergent to 0 actually
converges to 0', and that this equivalence holds with `provisionally' replaced by `negatively'. Finally, apparent convergence and convergence
are related by means of the anti-Specker principle.
Corrigendum to paper 112 (on game theory)
https://workdrive.zoho.com/file/v10n5fbbf506d7a424a80b3a1583922138672
As it stands, Theorem 3.2 of suffers from a hypothesis that is satisfied only in the case 1-by-1 games. This corrigendum removes that defect.
Feb. 2025: Expanded corrections to Techniques of Constructive Analysis (Book publication 7)
https://workdrive.zoho.com/file/f16vv8c41ca3ec3c24234b5bf81cf2512feb2
Correct version of Lemma 5.4.9 inTechniques of Constructive Analysis
https://workdrive.zoho.com/file/f16vv20df3d9680d04790abb647ed4fa5603f
The main point of this article is to present a corrected version of an important lemma in the constructive theory of locally convex spaces. We also outline some results, dealing with weak-star and weak-operator continuity of linear functionals, for whose proofs the lemma is important. The work is set in the framework of Bishop's constructive mathematics.
'On the Constructive Theory of Jordan Curves' arXiv:2502.09784v1
Douglas Sutherland Bridges
Professor Emeritus of Pure Mathematics, University of Canterbury, New Zealand
B.Sc. (Hons 1, Edinburgh); M.Sc. (Newcastle-upon-Tyne); Dip. Ed. (Edinburgh).
D.Phil. and D.Sc. (Oxford).
Fellow of the Royal Society of New Zealand
International Fellow of the Royal Society of Edinburgh
Born and brought up in Edinburgh, though I've lived in New Zealand for 35 years, I remain a proud Scot (and long-suffering supporter of Heart of Midlothian FC). I am a pure mathematician, though keenly interested in physics and mathematical economics, and have held academic posts at the University of Buckingham (1975–1989), the University of Waikato (1989–98), and the University of Canterbury (1999–2015). I retired from the last-named as Emeritus Professor in April 2015.
Vivien, my wife of 46 years, and I have three offspring - Iain, Hamish, and Catriona - and five grandchildren, three of whom live in the Northern Hemisphere, two in Christchurch.
My main research interest lies in constructive analysis, topology, and logic; I've also published a book and several papers in mathematical (micro)economics.
My primary interests outside mathematics are:
- music: singing in choirs and listening, with particular love for the keyboard music of Schubert, Beethoven, and Bach. (If you were allowed one piece of music to listen to before your execution, what would you choose? I'd probably go for the andante of Schubert's String Quintet D956; but Beethoven's Op. 111 sonata, Schubert's D959 or D960 sonatas, and Bach's Goldberg Variations would run it pretty close.)
- sport: football, cricket, and tennis.
- reading: philosophy, physics, and theology; biography (especially of American Presidents); detective fiction. My favourite authors of English literature are Shakespeare and Joseph Conrad. But the greatest novels I have read are probably Dostoevsky's The Brothers Karamazov and Crime and Punishment, Tolstoy's War and Peace and Anna Karenina, and Victor Hugo's Les Miserables.
By the way, the photo at the top of this website is one of James Clerk Maxwell, a son of Edinburgh, one of my great intellectual heroes. The photo immediately above the text is taken looking over Lake Wakatipu, New Zealand, towards the mountains above Glenorchy.
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