John Isbell

John Rolfe Isbell (born October 27, 1930 in Portland (Oregon) , † August 6, 2005 ) was an American mathematician.

He also published (first) under the collective pseudonym John Rainwater and under two other pseudonyms (MG Stanley, HC Enos).

Isbell was the son of an officer and attended different schools because of the changing stationing of his father. He studied at five colleges to a bachelor's degree and finally at the University of Chicago, among others with Irving Kaplansky , although in his own words Saunders Mac Lane , where he did not take courses, most influenced him. After Chicago (where he began his graduate studies after completing his bachelor's degree in 1951 but could not find an assistant position because he had received poor grades in differential geometry at SS Chern ) he was at Oklahoma State University , the University of Kansas at Lawrence and was at Princeton in 1954 University with Albert W. Tucker with a thesis on game theory ( Absolute Games ). At that time, however, he had already turned away from game theory and dealt with topology. Also in 1954 he did his military service in the Aberdeen Proving Ground . In 1956/57 and 1963/64 he was at the Institute for Advanced Study . He was at the University of Washington (Assistant Professor 1957 to 1959) and Case Western Reserve University (Professor 1965 to 1969). He died of complications from a failed biopsy performed a few years earlier.

Isbell was a professor at the State University of New York at Buffalo , where he taught as a professor from 1969. In 1999 he retired.

He dealt mainly with game theory, topology - with a monograph on uniform spaces - and category theory. He also dealt with abstract algebra and graph theory (the proof of the upper bound 7 in the number of colors in the Hadwiger-Nelson problem comes from Alexander Soifer von Isbell) and many other areas.

William Lawvere named 1986 Isbell conjugacy (Isbell conjugacy, also Isbell duality) in category theory after him.

Fonts (selection)

• Homogeneous spaces, Duke Math. J. Vol. 20, 1953, pp. 321-329, Project Euclid
• Zero-dimensional spaces, Tohoku Math. J., Volume 7, 1955, pp. 1-8
• Algebras of uniformly continuous functions, Annals of Mathematics, Volume 68, 1958, pp. 96-125
• Euclidean and weak uniformities, Pacific J. Math., Vol. 8. 1958, pp. 67-86
• On finite-dimensional uniform spaces, Pacific J. Math., Vol. 9, 1959, pp. 107-121
• Six theorems about injective metric spaces, Commentarii Mathematici Helvetici, Volume 39, 1964, pp. 65-76,
• Spaces without large projective subspaces, Math. Scand., Vol. 17, 1965, pp. 89-105
• Uniform spaces, AMS Math. Surveys, Volume 12, 1964
• General functorial semantics, American Journal of Mathematics, Volume 94, 1972, pp. 535-596
• Structure of categories, Bull. AMS, Vol. 72, 1966, pp. 619-655, Project Euclid
• Normal completion of categories, Reports of the Midwest Category Seminar, Volume 47, Springer 1967, pp. 110-155

literature

• Melvin Henriksen: John Isbell 1931-2005, TopCom (Topology Communications), Volume 11, 2006, online
• Interview with KD Magill, Topology Communications 1996 .

Individual evidence

1. ↑ Date and place of birth according to American Men and Women of Science , Thomson Gale 2004. Melvin Hendriksen incorrectly states 1931 in Topology Communications (see literature).
2. ↑ Date of death of obituaries Buffalo News , Aug. 28, 2005
3. ^ Robert Phelps: John Rainwater, TopCom, Volume 7, 2002, online
4. ↑ Interview with KD Magill, Topology Communications 1996, see Literatury
5. ↑ John Isbell in the Mathematics Genealogy Project (English)
6. ↑ Membership Book IAS 1980
7. ↑ Buffalo News 2005 death notification, after which he was professor there from 1969 to 1999
8. ↑ Alexander Soifer, The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of its Creators, Springer, 2008, p. 29. Isbell's result is from 1950.
9. ↑ Isbell duality, ncatlab