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Asymptotic values of some continuous mappings


Authors: A. Cantón and J. Qu
Journal: Proc. Amer. Math. Soc. 143 (2015), 2249-2252
MSC (2010): Primary 54C10
DOI: https://doi.org/10.1090/S0002-9939-2014-12391-4
Published electronically: December 22, 2014
MathSciNet review: 3314131
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Abstract: It is shown that the set of asymptotic values of a light continuous mapping defined on $ \mathbb{R}^s$ is an analytic set in the sense of Suslin.


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  • [1] Lennart Carleson, Selected problems on exceptional sets, Van Nostrand Mathematical Studies, No. 13, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0225986
  • [2] P. T. Church, Discrete maps on manifolds, Michigan Math. J. 25 (1978), no. 3, 351–357. MR 512905
  • [3] Thomas Jech, Set theory, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003. The third millennium edition, revised and expanded. MR 1940513
  • [4] S. Mazurkiewicz, Sur les points singuliers d'une fonction analytique, Fund. Math. 17 (1931), 26-29.
  • [5] B. Knaster and C. Kuratowski, Sur les ensembles connexes, Fund. Math. 2 (1921), 206-255.
  • [6] Seppo Rickman, Quasiregular mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 26, Springer-Verlag, Berlin, 1993. MR 1238941
  • [7] W. Sierpinski, Introduction to General Topology, University of Toronto Press, Toronto, 1934.
  • [8] Jussi Väisälä, Local topological properties of countable mappings, Duke Math. J. 41 (1974), 541–546. MR 0350688
  • [9] Matti Vuorinen, Conformal geometry and quasiregular mappings, Lecture Notes in Mathematics, vol. 1319, Springer-Verlag, Berlin, 1988. MR 950174

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Additional Information

A. Cantón
Affiliation: Departamento de Ciencias Aplicadas a la Ingeniería Naval, Universidad Politécnica de Madrid, Avda. Arco de la Victoria 4, 28040 Madrid, Spain
Email: alicia.canton@upm.es

J. Qu
Affiliation: Academy of Mathematics and System Science, Chinese Academy of Sciences, No. 55 East Zhongguancun Road, Beijing 100190, People’s Republic of China
Address at time of publication: Jinchunyuan West Building, Mathematical Science Center, Tsinghua University, Beijing 100080, People’s Republic of China
Email: qu11@math.purdue.edu, quijingjing@amss.ac.cn

DOI: https://doi.org/10.1090/S0002-9939-2014-12391-4
Received by editor(s): July 10, 2013
Received by editor(s) in revised form: October 18, 2013
Published electronically: December 22, 2014
Additional Notes: The first author was partially supported by a grant from Ministerio de Ciencia e Innovación (Spain), MTM 2009-07800. The second author performed her research while on leave from the Chinese Academy of Sciences and thanks Purdue University, and, in particular, Professor Drasin for his advice and hospitality. The second author was supported by NSFC Project 11271215.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2014 American Mathematical Society