Studies on dendrites and the periodic-recurrent property

Autores: Francisco Balibrea Gallego
Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 25, Nº 3, 2010 (Ejemplar dedicado a: Proceedings of the Seventh Italian-Spanish Conference of General Topology and its Applications, Badajoz (Spain), September 7-10, 2010), págs. 211-226
Idioma: inglés
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Resumen
- In this paper we evidence the interest of considering three outstanding examples of dendrites with different structures, dendrites F!, W and G3. When a dendrite X contains a topological copy of one of them, then it is derived important properties. For example, if X does not contain a topological copy neither F! nor W, then X is a tree. If X does not contain a topological copy of G3 then we obtain that X verifies the Periodic-Recurrent Property (the PR Property) which for dendrites is relevant under the point of view of Topological Dynamics. As an application of the former results, we give a unified proof of the fact that compact intervals of the real line [a; b] (a .= b), arcs and trees have also the PR Property.