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On composants of solenoids
Author(s):
Ronald
de Man
Journal:
Electron. Res. Announc. Amer. Math. Soc.
1
(1995),
87-90.
MSC (1991):
Primary 54F15;
Secondary 54F65, 54H20
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Abstract:
It is proved that any two composants of any two solenoids are homeomorphic.
References:
- 1
- J.M. Aarts, The structure of orbits in dynamical systems, Fund. Math. 129 (1988), 39-58. MR 89k:54092
- 2
- J.M. Aarts and R.J. Fokkink, The classification of solenoids, Proc. Amer. Math. Soc. 111 (1991), 1161-1163. MR 91g:54046
- 3
- R.H. Bing, A simple closed curve is the only homogeneous bounded plane continuum that contains an arc, Canad. J. Math. 12 (1960), 209-230. MR 22:1869
- 4
- C. Bandt, Composants of the horseshoe, Fund. Math. 144 (1994), 231-241.MR 95m:54034a
- 5
- D. van Dantzig, Ueber topologisch homogene Kontinua, Fund. Math. 15 (1930), 102-125.
- 6
- R.J. Fokkink, The structure of trajectories, PhD Thesis, Delft 1991.
- 7
- R.J. Fokkink, There exist uncountably many orbits in flows, Fund. Math. 136 (1990), 147-156. MR 92b:54082
- 8
- A. van Heemert, Topologische Gruppen und unzerlegbare Kontinua, Compositio Math. 5 (1938), 319-326.
- 9
- A.J. de Man, On composants of solenoids, Fund. Math. 147 (1995), 181-188. CMP 95:15
- 10
- M.C. McCord, Inverse limit sequences with covering maps, Trans. Amer. Math. Soc. 114 (1965), 197-209. MR 30:3450
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Additional Information:
Ronald
de Man
Affiliation:
Faculteit Wiskunde en Informatica, TU Eindhoven, Postbus 513, 5600 MB Eindhoven, The Netherlands
Email:
deman@win.tue.nl
DOI:
10.1090/S1079-6762-95-02005-1
PII:
S 1079-6762(95)02005-1
Received by editor(s):
June 26, 1995
Communicated by:
Krystyna Kuperberg
Copyright of article:
Copyright
1995,
American Mathematical Society
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