On open maps between dendrites

Academic Article

Abstract

  • In this paper we use a result by J. Krasinkiewicz to present a description of the topological behavior of an open map defined between dendrites. It is shown that, for every such map f: X → Y, there exist n subcontinua X 1, X 2, . . ., X n of X such that X = X 1 ∪ X 2 ∪ ⋯ ∪ X n, each set X i ∩ X j consists of at most one element which is a critical point of f, and each map f |Xi: X i →; Y is open, onto and can be lifted, in a natural way, to a product space Z i × Y for some compact and zero-dimensional space Z i. We also study the ω-limit sets ω(x) of a self-homeomorphism f: X → X defined on a dendrite X. It is shown that ω(x) is either a periodic orbit or a Cantor set (and if this is the case, then f |ω(x) is an adding machine). © 2007 University of Houston.
  • Authors

    Published In

    Author List

  • Acosta G; Eslami P; Oversteegen LG
  • Start Page

  • 753
  • End Page

  • 770
  • Volume

  • 33
  • Issue

  • 3