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A topological characterization of the dilation in $ E\sp{n}$


Author: L. S. Husch
Journal: Proc. Amer. Math. Soc. 28 (1971), 234-236
MSC: Primary 57.47
DOI: https://doi.org/10.1090/S0002-9939-1971-0283821-X
MathSciNet review: 0283821
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Abstract: A topological characterization is given to determine whether a homeomorphism of Euclidean $ n$-space, $ n \ne 4,5$, is topologically equivalent to the dilation $ x \to \frac{1}{2}x$.


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

  • [1] E. H. Connell, A topological $ H$-cobordism theorem for $ n \geqq 5$, Illinois J. Math. 11 (1967), 300-309. MR 35 #3673. MR 0212808 (35:3673)
  • [2] G. Higman, The units of group rings, Proc. London Math. Soc. (2) 46 (1940), 231-248. MR 2, 5. MR 0002137 (2:5b)
  • [3] P. J. Hilton and S. Wylie, Homology theory: An introduction to algebraic topology, Cambridge Univ. Press, New York, 1960. MR 22 #5963. MR 0115161 (22:5963)
  • [4] T. Homma and S. Kinoshita, On a topological characterization of the dilatation in $ {E^3}$, Osaka Math. J. 6 (1954), 135-144. MR 16, 160. MR 0063671 (16:160a)
  • [5] W. C. Hsiang and J. L. Shaneson, Fake tori, the annulus conjecture and the conjectures of Kirby, Proc. Nat. Acad. Sci. U.S.A. 62 (1969), 687-691. MR 0270378 (42:5267)
  • [6] B. v. Kerékjártó, Topologische Charakterisierung der linearen Abbildungen, Acta Litt. Acad. Sci. Szeged. 6 (1934), 235-262.
  • [7] S. Kinoshita, On quasi-translations in $ 3$-space, Topology of $ 3$-Manifolds and Related Topics (Proc. Univ. of Georgia Inst., 1961), Prentice-Hall, Englewood, Cliffs, N. J., 1962, pp. 223-226. MR 25 #3116. MR 0139685 (25:3116)
  • [8] -, Notes on covering transformation groups, Proc. Amer. Math. Soc. 19 (1968), 421-424. MR 36 #5921. MR 0222871 (36:5921)
  • [9] R. C. Kirby and L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742-749. MR 39 #3500. MR 0242166 (39:3500)
  • [10] L. C. Siebenmann, A total Whitehead torsion obstruction to fibering over the circle, Comment. Math. Helv. 45 (1970), 1-48. MR 0287564 (44:4768)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0283821-X
Keywords: Dilation, homeomorphisms of $ {E^n}$, regular homeomorphisms, equicontinuous powers, action of integers on $ {E^n}$
Article copyright: © Copyright 1971 American Mathematical Society

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