On composants of solenoids
Author:
Ronald de Man
Journal:
Electron. Res. Announc. Amer. Math. Soc. 1 (1995), 87-90
MSC (1991):
Primary 54F15; Secondary 54F65, 54H20
DOI:
https://doi.org/10.1090/S1079-6762-95-02005-1
MathSciNet review:
1350684
Full-text PDF Free Access
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Abstract: It is proved that any two composants of any two solenoids are homeomorphic.
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- A. van Heemert, Topologische Gruppen und unzerlegbare Kontinua, Compositio Math. 5 (1938), 319-326.
- A.J. de Man, On composants of solenoids, Fund. Math. 147 (1995), 181-188.
- M. C. McCord, Inverse limit sequences with covering maps, Trans. Amer. Math. Soc. 114 (1965), 197–209. MR 173237, DOI https://doi.org/10.1090/S0002-9947-1965-0173237-0
- J.M. Aarts, The structure of orbits in dynamical systems, Fund. Math. 129 (1988), 39-58.
- J.M. Aarts and R.J. Fokkink, The classification of solenoids, Proc. Amer. Math. Soc. 111 (1991), 1161-1163.
- 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.
- C. Bandt, Composants of the horseshoe, Fund. Math. 144 (1994), 231-241.
- D. van Dantzig, Ueber topologisch homogene Kontinua, Fund. Math. 15 (1930), 102-125.
- R.J. Fokkink, The structure of trajectories, PhD Thesis, Delft 1991.
- R.J. Fokkink, There exist uncountably many orbits in flows, Fund. Math. 136 (1990), 147-156.
- A. van Heemert, Topologische Gruppen und unzerlegbare Kontinua, Compositio Math. 5 (1938), 319-326.
- A.J. de Man, On composants of solenoids, Fund. Math. 147 (1995), 181-188.
- M.C. McCord, Inverse limit sequences with covering maps, Trans. Amer. Math. Soc. 114 (1965), 197-209.
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Additional Information
Ronald de Man
Email:
deman@win.tue.nl
Received by editor(s):
June 26, 1995
Article copyright:
© Copyright 1995
American Mathematical Society