Level sets of uniform quotient mappings from Rn to R do not need to be locally connected

• Autores: Beata Randrianantoanina
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 55, Fasc. 2, 2004, págs. 139-150
• Idioma: inglés
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• Resumen

  • We give an example of a uniform quotient map from $\mathbb{r}^ 2$ to $\mathbb{r}$ which has non-locally connected level sets.

• Referencias bibliográficas
  • S. Bates, W.B. Johnson, J. Lindenstrauss, D. Preiss, and G. Schechtman, Affine approximation of Lipschitz functions and nonlinear quotients,...
  • Y. Benyamini and J. Lindenstrauss, Geometric Nonlinear Functional Analysis, Vol. 1, American Mathematical Society, Providence, RI, 2000.
  • W.B. Johnson, J. Lindenstrauss, D. Preiss, and G. Schechtman, Uniform quotient mappings of the plane, Michigan Math. J. 47 (2000), 15–31.
  • K. Kuratowski, Topology, Vol. I, Academic Press, New York, 1966.
  • K. Kuratowski, Topology, Vol. II, Academic Press, New York, 1968.
  • O. Maleva, Components of level sets of uniform co-Lipschitz functions on the plane, Proc. Amer. Math. Soc. to appear.
  • B. Randrianantoanina, On the structure of level sets of uniform and Lipschitz quotient mappings from $\mathbb{R}^n$ to $\mathbb{R}$, Geom....
  • T. Terpai, Level sets of Lipschitz quotient mappings from $\mathbb{R}^n$ to $\mathbb{R}$, Preprint.
  • G.T. Whyburn, Analytic Topology, American Mathematical Society, Providence, R.I., 1963.