Factorials of infinite cardinals
John Dawson, Paul Howard (1976)
Fundamenta Mathematicae
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John Dawson, Paul Howard (1976)
Fundamenta Mathematicae
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J. Marshall Ash, A. Eduardo Gatto, Stephen Vági (1990)
Colloquium Mathematicae
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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.
L Moser (1959)
Acta Arithmetica
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A. Kucia, A. Szymański (1977)
Colloquium Mathematicae
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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.
Asit Baran-Raha (1972)
Colloquium Mathematicae
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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...
Tetsuya Ishiu, Justin Tatch Moore (2009)
Fundamenta Mathematicae
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We will characterize-under appropriate axiomatic assumptions-when a linear order is minimal with respect to not being a countable union of scattered suborders. We show that, assuming PFA⁺, the only linear orders which are minimal with respect to not being σ-scattered are either Countryman types or real types. We also outline a plausible approach to demonstrating the relative consistency of: There are no minimal non-σ-scattered linear orders. In the process of establishing these results,...
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.
H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)
Acta Arithmetica
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Zaslavski, Alexander J. (2002)
Abstract and Applied Analysis
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Walter H. Gottschalk (1964)
Annales de l'institut Fourier
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Jürg Schmid, Jürgen Schmidt (1987)
Colloquium Mathematicae
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A. Kanamori (1978)
Fundamenta Mathematicae
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