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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.

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 |