Mappings on the dyadic solenoid

Jan M. Aarts; Robbert J. Fokkink

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 4, page 697-699
  • ISSN: 0010-2628

Abstract

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Answering an open problem in [3] we show that for an even number k , there exist no k to 1 mappings on the dyadic solenoid.

How to cite

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Aarts, Jan M., and Fokkink, Robbert J.. "Mappings on the dyadic solenoid." Commentationes Mathematicae Universitatis Carolinae 44.4 (2003): 697-699. <http://eudml.org/doc/249156>.

@article{Aarts2003,
abstract = {Answering an open problem in [3] we show that for an even number $k$, there exist no $k$ to $1$ mappings on the dyadic solenoid.},
author = {Aarts, Jan M., Fokkink, Robbert J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Pontryagin duality; $k$ to $1$ maps; solenoids; Pontryagin duality; to 1 maps; solenoid},
language = {eng},
number = {4},
pages = {697-699},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Mappings on the dyadic solenoid},
url = {http://eudml.org/doc/249156},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Aarts, Jan M.
AU - Fokkink, Robbert J.
TI - Mappings on the dyadic solenoid
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 4
SP - 697
EP - 699
AB - Answering an open problem in [3] we show that for an even number $k$, there exist no $k$ to $1$ mappings on the dyadic solenoid.
LA - eng
KW - Pontryagin duality; $k$ to $1$ maps; solenoids; Pontryagin duality; to 1 maps; solenoid
UR - http://eudml.org/doc/249156
ER -

References

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  1. Aarts J.M., The structure of orbits in dynamical systems, Fund. Math. 129 (1988), 39-58. (1988) Zbl0664.54026MR0954894
  2. Aarts J.M., Fokkink R.J., The classification of solenoids, Proc. Amer. Math. Soc. 111 (1991), 1161-1163. (1991) Zbl0768.54026MR1042260
  3. Charatonik J.J., Covarrubias P.P., On covering mappings on solenoids, Proc. Amer. Math. Soc. 130 (2002), 2145-2154. (2002) Zbl0989.54038MR1896052
  4. Hewitt E., Ross K.A., Abstract Harmonic Analysis, Vol. I, Die Grundlehren der mathematischen Wissenschaften, Bd. 115, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. Zbl0837.43002MR0156915
  5. Krupski P., Means on solenoids, Proc. Amer. Math. Soc. 131 (2003), 1925-1929. (2003) Zbl1029.54041MR1955283
  6. Scheffer W.A., Maps between topological groups that are homotopic to homomorphisms, Proc. Amer. Math. Soc. 33 (1972), 562-567. (1972) Zbl0236.22008MR0301130
  7. Zhou Youcheng, Covering mappings on solenoids and their dynamical properties, Chinese Sci. Bull. 45 (2000), 1066-1070. (2000) MR1777211

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