Studies on dendrites and the periodic-recurrent property
ISSN: 0213-8743
Ano de publicación: 2010
Título do exemplar: Proceedings of the Seventh Italian-Spanish Conference of General Topology and its Applications, Badajoz (Spain), September 7-10, 2010
Volume: 25
Número: 3
Páxinas: 211-226
Tipo: Artigo
Outras publicacións en: Extracta mathematicae
Resumo
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.