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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2001 | 168 | 2 | 141-163

## Noninvertible minimal maps

EN

### Abstrakty

EN
For a discrete dynamical system given by a compact Hausdorff space X and a continuous selfmap f of X the connection between minimality, invertibility and openness of f is investigated. It is shown that any minimal map is feebly open, i.e., sends open sets to sets with nonempty interiors (and if it is open then it is a homeomorphism). Further, it is shown that if f is minimal and A ⊆ X then both f(A) and $f^{-1}(A)$ share with A those topological properties which describe how large a set is. Using these results it is proved that any minimal map in a compact metric space is almost one-to-one and, moreover, when restricted to a suitable invariant residual set it becomes a minimal homeomorphism. Finally, two kinds of examples of noninvertible minimal maps on the torus are given-these are obtained either as a factor or as an extension of an appropriate minimal homeomorphism of the torus.

141-163

wydano
2001

### Twórcy

autor
• Institute of Mathematics, Ukrainian Academy of Sciences, Tereshchenkivs'ka 3, 252601 Kiev, Ukraine
autor
• Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia
autor
• Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Santiago, Chile