Some applications of minimal open sets.
Nakaoka, Fumie, Oda, Nobuyuki (2001)
International Journal of Mathematics and Mathematical Sciences
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Nakaoka, Fumie, Oda, Nobuyuki (2001)
International Journal of Mathematics and Mathematical Sciences
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Karel Pastor, Dušan Bednařík (2001)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. 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...
Asit Baran-Raha (1972)
Colloquium Mathematicae
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Jürg Schmid, Jürgen Schmidt (1987)
Colloquium Mathematicae
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J. Marshall Ash, A. Eduardo Gatto, Stephen Vági (1990)
Colloquium Mathematicae
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L Moser (1959)
Acta Arithmetica
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Filippo Cammaroto, Andrei Catalioto, Jack Porter (2011)
Open Mathematics
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In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.
Zaslavski, Alexander J. (2002)
Abstract and Applied Analysis
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H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)
Acta Arithmetica
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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.
Michał Wiernowolski (1997)
Studia Mathematica
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We examine minimality in asymmetry classes of convex compact sets with respect to inclusion. We prove that each class has a minimal element. Moreover, we show there is a connection between asymmetry classes and the Rådström-Hörmander lattice. This is used to present an alternative solution to the problem of minimality posed by G. Ewald and G. C. Shephard in [4].