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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:
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[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
[5] Krupski P.: Means on solenoids. Proc. Amer. Math. Soc. 131 (2003), 1925-1929. MR 1955283 | Zbl 1029.54041
[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
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