R. H. Bing
RH Bing ( born October 20, 1914 in Oakwood, Texas, † April 28, 1986 in Austin, Texas) was an American mathematician who (especially three-dimensional ) dealt with general topology and geometric topology.
Life
Bing had really only the first names RH, which he preferred " RH" wrote. He grew up as the son of a teacher couple on (his father but later became a farmer ). Bing studied at Southwest Texas State Teachers College in 1935 and put the teachers exam from. He was then four years high school teacher in Texas. Besides, he continued to study mathematics at the University of Texas ( the reason he was then paid as a teacher later) and made his 1938 master's degree. In the same year he married. In 1943 he was instructor at the University of Texas where he earned his doctorate at Robert Lee Moore, 1945. 1949/50, he was at the University of Virginia and only then associate professor and then professor at the University of Wisconsin- Madison. In 1957/58, 1962/63 and 1967 he worked at the Institute for Advanced Study. In 1973 he went back to the University of Texas at Austin, where he was from 1975 to 1977 Chairman of the Mathematics Department and retired in 1985.
Bing was ( in the Council from 1970 to 1980 ) and 1966 and 1978, the U.S. representative in the International Mathematical Union. Since 1965 a member of the National Academy of Sciences 1977/78 he was president of the American Mathematical Society and 1963/64, the Mathematical Association of America. 1967 to 1969 he was chairman of the mathematics department at the National Research Council and from 1968 to 1975 in the National Science Board. In 1962 he was invited speaker at the International Congress of Mathematicians in Stockholm ( Embedding surfaces in 3- manifolds ).
Work
Bing is known through numerous works on geometric topology (particularly in the 1950s and 1960s ), which he in 1983 a summary textbook wrote. He tried several times on the Poincaré conjecture and proved in 1958 in this context that compact 3-manifolds are homeomorphic if and to the 3- sphere if every simple closed curve can be enclosed with a 3- ball in them. In 1957 he showed that two-dimensional surfaces in three-dimensional space by polyhedral surfaces can be approximated. In 1959 he gave a simpler proof ( than that of Edwin Moise ) of Triangulierbarkeit of 3-manifolds, where he applied his side Approximierungssatz ( "Side Approximation Theorem" ). Many sample designs and methods of topology are named after him (eg Bing 's Sticky Foot Topology, Bing 's Sling, Bing 's Hooked Rug, Bing Shrinking ) or designated by him (eg House with two rooms, dogbone space). In the general topology he described in 1951 metrizable spaces ( " Metrization of topological spaces", Canadian Journal of Mathematics 1951), in the Bing - Nagata - Smirnov Metrisierungstheorem ( Nagata and Smirnov published about it about the same time). One of his first successes was his solution to the " Kline Sphere Characterization Problem " from 1946 (Bulletin AMS, S.644 ), which states that a metric space that is shared by every simple closed curve in two parts, but not by any two points homeomorphic to the 2- sphere.
Writings
- The geometric topology of 3 - manifolds, AMS 1983
- Collected Papers, 2 volumes, AMS 1988