An elementary solution of the monotone mapping problem
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- by Joseph Martin and Ira Rosenholtz PDF
- Proc. Amer. Math. Soc. 72 (1978), 352-354 Request permission
Abstract:
A simple example of a monotone, noncompact mapping from ${{\mathbf {R}}^3}$ to ${{\mathbf {R}}^3}$ is constructed.References
- R. H. Bing, The monotone mapping problem, Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969) Markham, Chicago, Ill., 1970, pp.Β 99β115. MR 0275379 R. H. Bing and Joseph Martin, One-to-one maps of $E_ + ^3$, Proc. Binghamton Topology Conf., 1972.
- L. C. Glaser, Dimension lowering monotone non-compact mappings of $E^{n}$, Fund. Math. 58 (1966), 177β181. MR 193625, DOI 10.4064/fm-58-2-177-181
- L. C. Glaser, Monotone noncompact mappings of $E^{r}$ onto $E^{k}$ for $r\geq 4$ and $k\geq 3$, Proc. Amer. Math. Soc. 23 (1969), 282β286. MR 246270, DOI 10.1090/S0002-9939-1969-0246270-7
- G. T. Whyburn, Compactness of cetain mappings, Amer. J. Math. 81 (1959), 306β314. MR 111014, DOI 10.2307/2372746
Additional Information
- © Copyright 1978 American Mathematical Society
- 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