On composants of solenoids

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Faculteit Wiskunde en Informatica, TU Eindhoven, Postbus 513, 5600 MB Eindhoven, The Netherlands

It is proved that any two composants of any two solenoids are homeomorphic.

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, ibid. 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.
M. C. McCord, Inverse limit sequences with covering maps, Trans. Amer. Math. Soc. 114 (1965), 197-209.

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