On open maps between dendrites

• Autores: Gerardo Acosta, Peyman Eslami
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 3, 2007, págs. 753-770
• Idioma: inglés
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• Resumen

  • In this paper we mainly present two results, one dynamical and one topological, about open mappings between dendrites. The dynamical result states that if f is a homeomorphism from a dendrite X onto itself, then the omega limit set of any point of X is either a periodic orbit or a Cantor set. In the latter case, the restriction of f to this omega limit set is an adding machine. The topological result states that if f is an open map from a dendrite X onto a dendrite Y, then there exists n subcontinua X1, X2, ..., Xn of X such that X is the union of them, the intersection of any two of those subcontinua contains at most one element which is a critical point of f and the restriction of f to any set Xi is an open map from Xi onto Y that can be lifted, in a natural way, to a product space Zi x Y, for some compact and zero-dimensional space Zi