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R. H. Bing | |
|---|---|
| Born | (1914-10-20)October 20, 1914 |
| Died | April 28, 1986(1986-04-28) (aged 71) |
| Nationality | American |
| Alma mater | University of Texas at Austin |
| Known for | Bing–Borsuk conjecture Bing metrization theorem Bing's recognition theorem Bing shrinking Bing double |
| Scientific career | |
| Fields | Mathematics |
| Thesis | Concerning Simple Plane Webs (1945) |
| Doctoral advisor | Robert Lee Moore |
R. H. Bing (October 20, 1914 – April 28, 1986)[1] was an Americanmathematician who worked mainly in the areas ofgeometric topology andcontinuum theory. His father was named Rupert Henry, but Bing's mother thought that "Rupert Henry" was too British for Texas. She compromised by abbreviating it to R. H. (Singh 1986) Consequently, R. H. does not stand for a first or middle name.
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Bing's mathematical research was almost exclusively in 3-manifold theory and in particular, thegeometric topology of. The termBing-type topology was coined to describe the style of methods used by Bing.
Bing established his reputation early on in 1946, soon after completing his Ph.D. dissertation, by solving theKline sphere characterization problem. In 1948 he proved that thepseudo-arc ishomogeneous, contradicting a published but erroneous 'proof' to the contrary.
In 1951, he proved results regarding themetrizability of topological spaces, including what would later be called theBing–Nagata–Smirnov metrization theorem.
In 1952, Bing showed that the double of a solidAlexander horned sphere was the3-sphere. This showed the existence of aninvolution on the 3-sphere with fixed point set equal to a wildly embedded2-sphere, which meant that the originalSmith conjecture needed to be phrased in a suitable category. This result also jump-started research intocrumpled cubes. The proof involved a method later developed by Bing and others into set of techniques calledBing shrinking. Proofs of thegeneralized Schoenflies conjecture and thedouble suspension theorem relied on Bing-type shrinking.
Bing was fascinated by thePoincaré conjecture and made several major attacks which ended unsuccessfully, contributing to the reputation of the conjecture as a very difficult one. He did show that a simply connected, closed 3-manifold with the property that every loop was contained in a3-ball ishomeomorphic to the 3-sphere. Bing was responsible for initiating research into theProperty P conjecture, as well as its name, as a potentially more tractable version of the Poincaré conjecture. It was proven in 2004 as a culmination of work from several areas of mathematics. With some irony, this proof was announced some time afterGrigori Perelman announced his proof of the Poincaré conjecture.
Theside-approximation theorem was considered by Bing to be one of his key discoveries. It has many applications, including a simplified proof ofMoise's theorem, which states that every 3-manifold can be triangulated in an essentially unique way.
Thehouse with two rooms is a contractible 2-complex that is notcollapsible. Another such example, popularized byE.C. Zeeman, is thedunce hat.
The house with two rooms can also be thickened and then triangulated to be unshellable, despite the thickened house topologically being a 3-ball. The house with two rooms shows up in various ways in topology. For example, it is used in the proof that every compact 3-manifold has a standardspine.
Thedogbone space is thequotient space obtained from acellular decomposition of into points and polygonal arcs. The quotient space,, is not a manifold, but is homeomorphic to.
Bing was a visiting scholar at theInstitute for Advanced Study in 1957–58 and again in 1962–63.[2]
Bing served as president of theMAA (1963–1964), president of theAMS (1977–78), and was department chair atUniversity of Wisconsin, Madison (1958–1960), and atUniversity of Texas at Austin (1975–1977).
Before entering graduate school to study mathematics, Bing graduated from Southwest Texas State Teacher's College (known today asTexas State University), and was a high-school teacher for several years. His interest in education would persist for the rest of his life.
As mentioned in the introduction, Bing's father was named Rupert Henry, but Bing's mother thought that "Rupert Henry" was too British for Texas. Thus she compromised by abbreviating it to R. H. (Singh 1986)
It is told that once Bing was applying for a visa and was requested not to use initials. He explained that his name was really "R-only H-only Bing", and ended up receiving a visa made out to "Ronly Honly Bing".[5]
