Journal of Fixed Point Theory and Applications

, Volume 17, Issue 3, pp 495–505 | Cite as

On local fixed or periodic point properties

  • Alejandro Illanes
  • Paweł Krupski
Open Access


A space X has the local fixed point property LFPP (resp., local periodic point property LPPP) if it has an open basis \({\mathcal{B}}\) such that, for each \({B \in \mathcal{B}}\), the closure \({\overline{B}}\) has the fixed (resp., periodic) point property. Weaker versions wLFPP, wLPPP are also considered and examples of metric continua that distinguish all these properties are constructed. We show that for planar or one-dimensional locally connected metric continua the properties are equivalent.


Local fixed point property local periodic point property locally connected continuum 

Mathematics Subject Classification

Primary 37B45 Secondary 54F15 


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Copyright information

© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de México, Circuito Exterior, Ciudad UniversitariaMéxicoMexico
  2. 2.Institute of MathematicsUniversity of WrocławWrocławPoland

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