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Ukrainian Mathematical Journal

, Volume 66, Issue 2, pp 197–208 | Cite as

Topologically Mixing Maps and the Pseudoarc

  • T. Drwiega
  • P. Oprocha
Article
  • 75 Downloads

It is known that the pseudoarc can be constructed as the inverse limit of the copies of [0, 1] with one bonding map f which is topologically exact. On the other hand, the shift homeomorphism σ f is topologically mixing in this case. Thus, it is natural to ask whether f can be only mixing or must be exact. It has been recently observed that, in the case of some hereditarily indecomposable continua (e.g., pseudocircles) the property of mixing of a bonding map implies its exactness. The main aim of the present article is to show that the indicated kind of forcing of recurrence is not the case for the bonding map defining the pseudoarc.\

Keywords

Topological Entropy Inverse Limit Topological Graph Positive Topological Entropy Linear Homeomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • T. Drwiega
    • 1
  • P. Oprocha
    • 1
    • 2
  1. 1.AGH University of Sciences and TechnologyKrakówPoland
  2. 2.Institute of MathematicsPolish Academy of SciencesWarszawaPoland

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