Bing, R. H.
Overview
Works:  41 works in 116 publications in 2 languages and 1,484 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Honoree, Contributor 
Classifications:  QA611, 513.83 
Publication Timeline
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Most widely held works about
R. H Bing
 The collected papers of R.H. Bing by R. H Bing( Book )
 R. H. Bing Papers by R. H Bing( )
 Moore, R.L., Papers by R. L Moore( )
 The Collected papers by R. H Bing( Book )
 A new proof that 1ULC implies tameness by Davis Wallace Finley( )
 Anderson, Bruce A., papers by Bruce A Anderson( )
 Bing, R.H., Papers by R. H Bing( )
 Special volume in honor of R.H. Bing (19141986)( )
 R.H. Bing interview by R. H Bing( )
 R. H. Bing Papers by R. H Bing( )
 Henderson, David W., papers by David W Henderson( )
 A converse of a theorem of R.H. Bing and its generalization; technical note by Raymond Louis Wilder( Book )
 R.H. Bing October 20, 1914April 28, 1986 by Michael P Starbird( )
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Most widely held works by
R. H Bing
Topology Seminar, Wisconsin, 1965 by
R. H Bing(
Book
)
29 editions published in 1966 in 3 languages and held by 484 WorldCat member libraries worldwide
29 editions published in 1966 in 3 languages and held by 484 WorldCat member libraries worldwide
The geometric topology of 3manifolds by
R. H Bing(
Book
)
15 editions published between 1970 and 2001 in English and held by 426 WorldCat member libraries worldwide
This is a summary of four Colloquium Lectures given at the meeting of the American Mathematical Society in Laramie in 1970. The first section discusses the recent solution of the monotone mapping theorem. The second discusses difficulty and headway in extending results about 3manifolds to those of higher dimensions. The last two sections discuss approximation theorems and their applications. (Author)
15 editions published between 1970 and 2001 in English and held by 426 WorldCat member libraries worldwide
This is a summary of four Colloquium Lectures given at the meeting of the American Mathematical Society in Laramie in 1970. The first section discusses the recent solution of the monotone mapping theorem. The second discusses difficulty and headway in extending results about 3manifolds to those of higher dimensions. The last two sections discuss approximation theorems and their applications. (Author)
Continua, decompositions, manifolds : proceedings of Texas Topology Symposium, 1980 by Texas Toplogy Symposium(
Book
)
8 editions published in 1983 in English and held by 209 WorldCat member libraries worldwide
8 editions published in 1983 in English and held by 209 WorldCat member libraries worldwide
Elementary point set topology by
R. H Bing(
Book
)
5 editions published in 1960 in English and held by 60 WorldCat member libraries worldwide
5 editions published in 1960 in English and held by 60 WorldCat member libraries worldwide
Computing the fundamental group of the complements of curves by
R. H Bing(
Book
)
2 editions published in 1965 in English and held by 21 WorldCat member libraries worldwide
2 editions published in 1965 in English and held by 21 WorldCat member libraries worldwide
The collected papers of R.H. Bing by
R. H Bing(
Book
)
6 editions published in 1988 in English and held by 20 WorldCat member libraries worldwide
6 editions published in 1988 in English and held by 20 WorldCat member libraries worldwide
The Collected papers by
R. H Bing(
Book
)
6 editions published in 1988 in English and Undetermined and held by 15 WorldCat member libraries worldwide
6 editions published in 1988 in English and Undetermined and held by 15 WorldCat member libraries worldwide
The Collected papers by
R. H Bing(
Book
)
3 editions published in 1988 in English and Undetermined and held by 9 WorldCat member libraries worldwide
3 editions published in 1988 in English and Undetermined and held by 9 WorldCat member libraries worldwide
Proceedings by Topology Seminar(
Book
)
1 edition published in 1966 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1966 in English and held by 4 WorldCat member libraries worldwide
Wild surfaces have some nice properties by
R. H Bing(
Book
)
1 edition published in 1985 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1985 in English and held by 3 WorldCat member libraries worldwide
Extending Monotone Decompositions of 3Manifolds by
R. H Bing(
Book
)
2 editions published in 1971 in English and held by 2 WorldCat member libraries worldwide
It is shown that if Y is a closed subset of Euclidean 3space E sup 3 such that each component of Y is compact but does not separate E sup 3, then there is a compact monotone map of E sup 3 onto itself such that the components of Y are point inverses and the nondegenerate point inverses not in Y are polyhedral 1complexes. (Author)
2 editions published in 1971 in English and held by 2 WorldCat member libraries worldwide
It is shown that if Y is a closed subset of Euclidean 3space E sup 3 such that each component of Y is compact but does not separate E sup 3, then there is a compact monotone map of E sup 3 onto itself such that the components of Y are point inverses and the nondegenerate point inverses not in Y are polyhedral 1complexes. (Author)
Cubes with Knotted Holes by
R. H Bing(
Book
)
2 editions published in 1971 in English and held by 2 WorldCat member libraries worldwide
The 3dimensional Poincare conjecture is that a compact, connected, simply connected 3manifold without boundary is topologically a 3sphere S sup 3. Despite efforts to prove the conjecture, it has withstood attack. It is known that every orientable 3manifold may be obtained by removing a collection of disjoint solid tori from S sup 3 and sewing them back differently. In this paper the author examine some of the possibilities for constructing a counterexample to the Poincare conjecture by removing a single solid torus from S sup 3 and sewing it back differently. Actually, they examine not only this process but one analogous to it which they call 'attaching a pillbox to a cube with a knotted hole.' (Author)
2 editions published in 1971 in English and held by 2 WorldCat member libraries worldwide
The 3dimensional Poincare conjecture is that a compact, connected, simply connected 3manifold without boundary is topologically a 3sphere S sup 3. Despite efforts to prove the conjecture, it has withstood attack. It is known that every orientable 3manifold may be obtained by removing a collection of disjoint solid tori from S sup 3 and sewing them back differently. In this paper the author examine some of the possibilities for constructing a counterexample to the Poincare conjecture by removing a single solid torus from S sup 3 and sewing it back differently. Actually, they examine not only this process but one analogous to it which they call 'attaching a pillbox to a cube with a knotted hole.' (Author)
The collected papers of R. H. Bing by
R. H Bing(
Book
)
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
The monotone mapping problem by
R. H Bing(
Book
)
2 editions published in 1971 in English and held by 2 WorldCat member libraries worldwide
It is shown that for m = 3,4 ... there is a monotone map of Euclidean n space E sup n onto itself that is not compact. This completes the monotone mapping theorem posed by G.T. Whyburn. A key lemma in the treatment shows that there is a monotone map of a cube I sup 2 onto itself such that each point inverse intersects a base I sup 2 of I sup 3. If f is a map of I sup 3 onto I sup 3 which is a homeomorphism on Int I sup 3 and takes I sup 2 homeomorphically into I sup 2, one calls f (Int I sup 2 joined to Int I sup 3) a drainage system for I sup 3. It is shown that there is a drainage system f (Int I sup 2 joined to Int I sup 3) for I sup 3 and a monotone map g of I sup 3  f (Int I sup 2 joined to Int I sup 3) onto I sup 3 such that g is the identity on Bd I sup 3  Int I sup 2. (Author)
2 editions published in 1971 in English and held by 2 WorldCat member libraries worldwide
It is shown that for m = 3,4 ... there is a monotone map of Euclidean n space E sup n onto itself that is not compact. This completes the monotone mapping theorem posed by G.T. Whyburn. A key lemma in the treatment shows that there is a monotone map of a cube I sup 2 onto itself such that each point inverse intersects a base I sup 2 of I sup 3. If f is a map of I sup 3 onto I sup 3 which is a homeomorphism on Int I sup 3 and takes I sup 2 homeomorphically into I sup 2, one calls f (Int I sup 2 joined to Int I sup 3) a drainage system for I sup 3. It is shown that there is a drainage system f (Int I sup 2 joined to Int I sup 3) for I sup 3 and a monotone map g of I sup 3  f (Int I sup 2 joined to Int I sup 3) onto I sup 3 such that g is the identity on Bd I sup 3  Int I sup 2. (Author)
Coverings with connected intersections by
R. H Bing(
Book
)
1 edition published in 1950 in English and held by 1 WorldCat member library worldwide
1 edition published in 1950 in English and held by 1 WorldCat member library worldwide
The mathematics that juniorhighschool pupils use by
R. H Bing(
)
1 edition published in 1938 in English and held by 1 WorldCat member library worldwide
1 edition published in 1938 in English and held by 1 WorldCat member library worldwide
Monotone Image of E Superscript 3(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
Using the fact that there is a monotone map of a cube onto itself such that each point inverse intersects the boundary, it is shown that there is a compact monotone map of Euclidean 3space E sup 3 onto any compact connected 3manifold whatsoever. Alternative methods are given for describing these maps. (Author)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
Using the fact that there is a monotone map of a cube onto itself such that each point inverse intersects the boundary, it is shown that there is a compact monotone map of Euclidean 3space E sup 3 onto any compact connected 3manifold whatsoever. Alternative methods are given for describing these maps. (Author)
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Related Identities
 Armentrout, Steve Author Editor
 Bean, R. J. (Ralph J.) Contributor Editor
 University of Wisconsin
 Singh, Sukhjit Editor
 Starbird, Michael P. Author Editor
 University of Texas at Austin
 Eaton, William T. Editor
 Daverman, Robert J. Editor
 Washington State University Department of Mathematics
 University of WisconsinMilwaukee
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Associated Subjects
American Mathematical Society Approximation theory Archibald, Raymond Clare, Arithmetic Armentrout, Steve Beckenbach, Edwin F Bell, Eric Temple, Bing, R. H Birkhoff, Garrett, Bliss, Gilbert Ames, Bôcher, Maxime, Chittenden, Edward Wilson Combinatorial analysis Continuity Curves, Algebraic Decomposition (Mathematics) Dickson, Leonard E.(Leonard Eugene), Dissertations, Academic Embedding theorems Fréchet, Maurice, Halsted, George Bruce, Interviews Junior high schools Knot theory Kuratowski, Kazimierz, Lefschetz, Solomon, Manifolds (Mathematics) Mathematicians MathematicsStudy and teaching Moore, Eliakim Hastings, Moore, R. L.(Robert Lee), Richardson, R. G. D.(Roland George Dwight), Rudin, Mary Ellen, Set theory Stone, Marshall H.(Marshall Harvey), Threemanifolds (Topology) Topology United States University of WisconsinMadison.Mathematics Department Veblen, Oswald, Whyburn, Gordon Thomas, Wilder, Raymond Louis,