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Journal of Mathematical Sciences

, Volume 215, Issue 3, pp 376–386 | Cite as

The Fixed-Point Property Under Induced Interval Maps of Continua

  • D. Robatian
Article
  • 49 Downloads

Let f : I → I be a continuous map of a compact interval I and let C(I) be hyperspace of all compact subintervals of I equipped with the Hausdorff metric. We study the fixed-point property of the subsets of C (I) with respect to any induced interval map ℱ : C (I) → C (I). In particular, we prove that any nonempty subcontinuum of C (I) possesses the fixed-point property.

Keywords

Compact Interval Connected Subset Monotone Sequence Lower Vertex Compact Subinterval 
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 2016

Authors and Affiliations

  • D. Robatian
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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