On covering mappings on solenoids
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- by Janusz J. Charatonik and Patricia Pellicer Covarrubias PDF
- Proc. Amer. Math. Soc. 130 (2002), 2145-2154 Request permission
Abstract:
Covering mappings on the dyadic solenoid are studied. Some results stated by Zhou Youcheng (2000) are discussed in a more detailed way by indicating certain inaccuracies in their proofs. These are either corrected or supplemented, or else suitable counterexamples are constructed. Some open questions are asked and connections with related results are considered.References
- Wojciech Dębski, Two-to-one maps on solenoids and Knaster continua, Fund. Math. 141 (1992), no. 3, 277–285. MR 1199240, DOI 10.4064/fm-141-3-277-285
- Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
- K. R. Gentry, Some properties of the induced map, Fund. Math. 66 (1969/70), 55–59. MR 253276, DOI 10.4064/fm-66-1-55-59
- Jo W. Heath, Each locally one-to-one map from a continuum onto a tree-like continuum is a homeomorphism, Proc. Amer. Math. Soc. 124 (1996), no. 8, 2571–2573. MR 1371127, DOI 10.1090/S0002-9939-96-03736-7
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
- T. Maćkowiak, Local homeomorphisms onto tree-like continua, Colloq. Math. 38 (1977), no. 1, 63–68. MR 464200, DOI 10.4064/cm-38-1-63-68
- Sam B. Nadler Jr., Continuum theory, Monographs and Textbooks in Pure and Applied Mathematics, vol. 158, Marcel Dekker, Inc., New York, 1992. An introduction. MR 1192552
- E. Puzio, Limit mappings and projections of inverse systems, Fund. Math. 80 (1973), no. 1, 57–73. MR 345052, DOI 10.4064/fm-80-1-57-73
- J. J. Corliss, Upper limits to the real roots of a real algebraic equation, Amer. Math. Monthly 46 (1939), 334–338. MR 4
- Zhou Youcheng, Covering mapping on solenoids and their dynamical properties, Chinese Sci. Bull. 45 (2000), 1066–1070.
Additional Information
- Janusz J. Charatonik
- Affiliation: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland – and – Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
- Email: jjc@matem.unam.mx
- Patricia Pellicer Covarrubias
- Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
- Email: pellicer@matem.unam.mx
- Received by editor(s): November 30, 2000
- Received by editor(s) in revised form: January 30, 2001
- Published electronically: December 20, 2001
- Communicated by: Alan Dow
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2145-2154
- MSC (2000): Primary 54F15
- DOI: https://doi.org/10.1090/S0002-9939-01-06296-7
- MathSciNet review: 1896052