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An elementary solution of the monotone mapping problem


Authors: Joseph Martin and Ira Rosenholtz
Journal: Proc. Amer. Math. Soc. 72 (1978), 352-354
MSC: Primary 54C10; Secondary 57N12
DOI: https://doi.org/10.1090/S0002-9939-1978-0507337-4
MathSciNet review: 507337
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Abstract: A simple example of a monotone, noncompact mapping from $ {{\mathbf{R}}^3}$ to $ {{\mathbf{R}}^3}$ is constructed.


References [Enhancements On Off] (What's this?)

  • [1] R. H. Bing, The monotone mapping problem, Topology of Manifolds (J. C. Cantrell and C. H. Edwards, eds.), Markham, Chicago, pp. 99-115. MR 0275379 (43:1136)
  • [2] R. H. Bing and Joseph Martin, One-to-one maps of $ E_ + ^3$, Proc. Binghamton Topology Conf., 1972.
  • [3] L. C. Glaser, Dimension lowering monotone non-compact mappings of $ {E^n}$, Fund. Math. 58 (1966), 177-181. MR 0193625 (33:1841)
  • [4] -, Monotone non-compact mappings of $ {E^r}$ onto $ {E^k}$ for $ r \geqslant 4$ and $ k \geqslant 3$, Proc. Amer. Math. Soc. 23 (1969), 282-286. MR 0246270 (39:7574)
  • [5] G. T. Whyburn, Compactness of certain mappings, Amer. J. Math. 81 (1959), 306-314. MR 0111014 (22:1881)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0507337-4
Keywords: Monotone Mapping Problem, monotone map, compact map
Article copyright: © Copyright 1978 American Mathematical Society

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