| Title:
|
Mappings on the dyadic solenoid (English) |
| Author:
|
Aarts, Jan M. |
| Author:
|
Fokkink, Robbert J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
697-699 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Pontryagin duality |
| Keyword:
|
$k$ to $1$ maps |
| Keyword:
|
solenoids |
| MSC:
|
22C05 |
| MSC:
|
54F15 |
| idZBL:
|
Zbl 1099.22005 |
| idMR:
|
MR2062886 |
| . |
| Date available:
|
2009-01-08T19:32:18Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119424 |
| . |
| Reference:
|
[1] Aarts J.M.: The structure of orbits in dynamical systems.Fund. Math. 129 (1988), 39-58. Zbl 0664.54026, MR 0954894 |
| Reference:
|
[2] Aarts J.M., Fokkink R.J.: The classification of solenoids.Proc. Amer. Math. Soc. 111 (1991), 1161-1163. Zbl 0768.54026, MR 1042260 |
| Reference:
|
[3] Charatonik J.J., Covarrubias P.P.: On covering mappings on solenoids.Proc. Amer. Math. Soc. 130 (2002), 2145-2154. Zbl 0989.54038, MR 1896052 |
| Reference:
|
[4] Hewitt E., Ross K.A.: Abstract Harmonic Analysis.Vol. I, Die Grundlehren der mathematischen Wissenschaften, Bd. 115, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. Zbl 0837.43002, MR 0156915 |
| Reference:
|
[5] Krupski P.: Means on solenoids.Proc. Amer. Math. Soc. 131 (2003), 1925-1929. Zbl 1029.54041, MR 1955283 |
| Reference:
|
[6] Scheffer W.A.: Maps between topological groups that are homotopic to homomorphisms.Proc. Amer. Math. Soc. 33 (1972), 562-567. Zbl 0236.22008, MR 0301130 |
| Reference:
|
[7] Zhou Youcheng: Covering mappings on solenoids and their dynamical properties.Chinese Sci. Bull. 45 (2000), 1066-1070. MR 1777211 |
| . |
