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On covering mappings on solenoids
Author(s):
Janusz
J.
Charatonik;
Patricia
Pellicer
Covarrubias
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2145-2154.
MSC (2000):
Primary 54F15
Posted:
December 20, 2001
MathSciNet review:
1896052
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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:
-
- 1.
- W. Debski, Two-to-one maps on solenoids and Knaster continua, Fund. Math. 141 (1992), 277-285. MR 94b:54094
- 2.
- R. Engelking, General topology, Heldermann Verlag, Berlin, 1989. MR 91c:54001
- 3.
- K. R. Gentry, Some properties of the induced map, Fund. Math. 66 (1969), 55-59. MR 40:6491
- 4.
- J. 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), 2571-2573. MR 97c:54016
- 5.
- K. Kuratowski, Topology, vol. 1, Academic Press and PWN, New York, London and Warszawa, 1966. MR 36:840
- 6.
- T. Mackowiak, Local homeomorphisms onto tree-like continua, Colloq. Math. 38 (1977), 63-68. MR 57:4135
- 7.
- S. B. Nadler, Jr., Continuum theory, M. Dekker, New York, Basel and Hong Kong, 1992. MR 93m:54002
- 8.
- E. Puzio, Limit mappings and projections of inverse systems, Fund. Math. 80 (1973), 57-73. MR 49:9791
- 9.
- G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ. 28, Providence, 1942; reprinted with corrections, 1971. MR 4:86b; MR 32:425
- 10.
- Zhou Youcheng, Covering mapping on solenoids and their dynamical properties, Chinese Sci. Bull. 45 (2000), 1066-1070. CMP 2000:17
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Additional Information:
Janusz
J.
Charatonik
Affiliation:
Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, 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
DOI:
10.1090/S0002-9939-01-06296-7
PII:
S 0002-9939(01)06296-7
Keywords:
Continuum,
covering mapping,
homotopic,
inverse limit,
solenoid
Received by editor(s):
November 30, 2000
Received by editor(s) in revised form:
January 30, 2001
Posted:
December 20, 2001
Communicated by:
Alan Dow
Copyright of article:
Copyright
2001,
American Mathematical Society
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