Anthony Morse

Anthony Perry Morse, Berkeley 1968

Anthony Perry Morse (born August 21, 1911 in Ithaca , New York , † 1984 ) was an American mathematician who dealt with topology, analysis and especially measure theory .

Life

Morse went to school in Ithaca (New York) , studied at Cornell University and received his doctorate in 1937 under Clarence Raymond Adams at Brown University (Convergence in variation and related topics). As a post-doctoral researcher had he spent two years (until 1939) at the Institute for Advanced Study , and then at the University of California, Berkeley , where he became a professor. During the Second World War he worked as a ballistician on the Aberdeen Proving Ground , where he developed, among other things, ballistic panels for air-to-surface missiles. The height of his influence at Berkeley was in the early 1950s when he developed a close relationship with his graduate students and also played a large role in the university's social life. That changed in 1960 after his second marriage when he moved to Orinda from Berkeley. He was rarely on campus, while at the same time the math faculty was highly diversified and dominated by other mathematicians. In 1972 he retired.

In the McCarthy era , he was one of 29 faculty members at Berkeley who refused to take the oath of loyalty. (These also included Ernst Kantorowicz and Gian Carlo Wick ).

plant

He is known for Morse-Kelly set theory , an axiomatization of set theory introduced by John L. Kelley (in the appendix to his book General Topology of 1955) and Anthony Morse (presented by Morse in 1965 in his book A theory of sets , however in an idiosyncratic notation). The theory was presented by Hao Wang in 1949 and uses ideas from Willard Van Orman Quine . The theory is an extension of the Zermelo-Fraenkel set theory and related to the Neumann-Bernays-Gödel set theory and, like these, contains classes as elements in addition to sets.

The set of Sard ( Arthur Sard 1942) differential topology is sometimes called, in addition to Morse, as he proved a special case in 1939, who then gave him great recognition. In 1943 he and Herbert Federer proved the theorem of Federer and Morse in measure theory . Let be a surjective continuous mapping between compact metric spaces . Then there is a Borel set such that the restriction of f is to a bijective mapping of on . ${\displaystyle f\colon X\to Y}$ ${\displaystyle X,Y}$ ${\displaystyle Z\subset X}$ ${\displaystyle Z}$ ${\displaystyle Z}$ ${\displaystyle Y}$

He also made contributions to the Banach-Tarski paradox by showing that there is no such paradoxical decomposition in the plane for a broad class of sets as in three-dimensional space.

Herbert Federer and Woody Bledsoe are among his PhD students .

In mathematics, he also attached importance to formal accuracy beyond the usual and considered himself a toolmaker of exact systems of the fundamentals of mathematics (set theory, logic). His formal systems should also be computer-programmable. The motive was also behind his development of Morse-Kelly set theory in the 1960s, but he worked on it for decades until his death.

Others

His father was a very successful inventor and Morse developed and edited the installations in almost every house he lived in. He was even commissioned by a plumber in Berkeley to install a heating system developed by Morse himself in his own house.

Fonts

• A theory of sets, Academic Press 1965, 2nd edition 1986

Web links

• Obituary by Beesley, Kelley, Lewy, McMinn, University of California (English)

Individual evidence

1. ↑ Anthony Morse in the Mathematics Genealogy Project (English)
2. ^ Non Signers List, University of California Berkeley
3. ↑ He traces the theory back to Thoralf Skolem and Anthony Morse.
4. ↑ Morse, The behavior of a function on its critical set, Annals of Mathematics, Volume 40, 1939, pp. 62-70
5. ↑ Federer, Morse, Some Properties of Measurable Functions, Bulletin of the American Mathematical Society, Volume 49, 1943, pp. 270-277
6. ^ University of California: In Memoriam, 1987. In: content.cdlib.org. Retrieved August 24, 2015 .