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Errett Bishop: reflections on him and his research. (Proceedings of the Memorial Meeting for Errett Bishop held at the University of California, San Diego, September 24, 1983). (English) Zbl 0579.01015

Contemporary Mathematics, 39. Providence, R.I.: American Mathematical Society (AMS). XVII, 91 p. $ 16.00 (1985).
The object of this memorial volume is to present a view of Errett Bishop - who died april 14, 1983 - as an individual, a colleague and a mathematician. Besides a curriculum vitae there is a list of 34 publications by Bishop, 27 of which are on measures, function algebras and functions of several complex variables, and 7 on constructive mathematics. The volume opens with E. Bishop’s inspiring paper on constructive mathematics ”Schizophrenia in contemporary mathematics” (pp. 1-32), dating from 1973. It summarizes some of the main questions at the time of its composition and is still worth reading. In the meantime there has appeared a thorough revision of Bishop’s ”Foundations of constructive mathematics” (1967; Zbl 0183.015), viz. E. Bishop, D. Bridges: Constructive Analysis (1985).
Bishop’s paper is followed by a number of contributions on Bishop’s influence on the domains of mathematics in which he worked. There is an ”In memoriam” by S. Warschawski (pp. 33-39), ”Recollections” by J. Kelley (pp. 51-55) and ”Remembrances of Errett Bishop” by A. Nerode, G. Metakides and R. Constable (pp. 79-84), who trace Bishop’s influence on the origin of their theorem proving programming languages for constructive mathematics.
J. Wermer (”The work of Errett Bishop in several complex variables”, pp. 41-50) describes Bishop’s work on functions of several complex variables and I. Glicksberg his work on uniform algebras (”The work of Errett Bishop and uniform algebras”, pp. 65-78). These papers cover the greater part of Bishop’s work in classical mathematics.
In ”Aspects of constructive analysis” (pp. 57-64), H. Royden presents some of his own results in relation to Bishop’s constructivism, and in ”On Bishop’s Hahn-Banach Theorem” (pp. 85-91), G. Metakides, A. Nerode and R. A. Shore treat a recursive version of the Hahn-Banach theorem. Despite its modest outlook and size this is a beautiful memorial to Errett Bishop.
Reviewer: B.van Rootselaar

MSC:

01A70 Biographies, obituaries, personalia, bibliographies
03-03 History of mathematical logic and foundations
03-06 Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations
00B25 Proceedings of conferences of miscellaneous specific interest

Biographic References:

Bishop, Errett

Citations:

Zbl 0183.015
Full Text: DOI