Minimal realcompact spaces
Asit Baran-Raha (1972)
Colloquium Mathematicae
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Asit Baran-Raha (1972)
Colloquium Mathematicae
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H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)
Acta Arithmetica
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L Moser (1959)
Acta Arithmetica
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Pierre Michel (1975)
Publications mathématiques et informatique de Rennes
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Dusa McDuff (1981)
Annales de l'institut Fourier
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Necessary conditions are found for a Cantor subset of the circle to be minimal for some -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.
Aikawa, Hiroaki (1993)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Tomasz Downarowicz (2011)
Colloquium Mathematicae
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We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our...
Jürg Schmid, Jürgen Schmidt (1987)
Colloquium Mathematicae
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Khalil, R. (2002)
Rendiconti del Seminario Matematico
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Walter H. Gottschalk (1964)
Annales de l'institut Fourier
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Zaslavski, Alexander J. (2002)
Abstract and Applied Analysis
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Dariusz Tywoniuk (2012)
Colloquium Mathematicae
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We construct a continuous non-invertible minimal transformation of an arbitrary solenoid. Since solenoids, as all other compact monothetic groups, also admit minimal homeomorphisms, our result allows one to classify solenoids among continua admitting both invertible and non-invertible continuous minimal maps.
Stanimirović, Predrag S. (2000)
Novi Sad Journal of Mathematics
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Henk Bruin, Sergiǐ Kolyada, L'ubomír Snoha (2003)
Colloquium Mathematicae
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We show that there are (1) nonhomogeneous metric continua that admit minimal noninvertible maps but have the fixed point property for homeomorphisms, and (2) nonhomogeneous metric continua that admit both minimal noninvertible maps and minimal homeomorphisms. The former continua are constructed as quotient spaces of the torus or as subsets of the torus, the latter are constructed as subsets of the torus.