Article
Keywords:
Pontryagin duality; $k$ to $1$ maps; solenoids
Summary:
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.
References:
[1] Aarts J.M.:
The structure of orbits in dynamical systems. Fund. Math. 129 (1988), 39-58.
MR 0954894 |
Zbl 0664.54026
[2] Aarts J.M., Fokkink R.J.:
The classification of solenoids. Proc. Amer. Math. Soc. 111 (1991), 1161-1163.
MR 1042260 |
Zbl 0768.54026
[3] Charatonik J.J., Covarrubias P.P.:
On covering mappings on solenoids. Proc. Amer. Math. Soc. 130 (2002), 2145-2154.
MR 1896052 |
Zbl 0989.54038
[4] Hewitt E., Ross K.A.:
Abstract Harmonic Analysis. Vol. I, Die Grundlehren der mathematischen Wissenschaften, Bd. 115, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963.
MR 0156915 |
Zbl 0837.43002
[6] Scheffer W.A.:
Maps between topological groups that are homotopic to homomorphisms. Proc. Amer. Math. Soc. 33 (1972), 562-567.
MR 0301130 |
Zbl 0236.22008
[7] Zhou Youcheng:
Covering mappings on solenoids and their dynamical properties. Chinese Sci. Bull. 45 (2000), 1066-1070.
MR 1777211