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The Closed Subset Theorem for Inverse Limits with Upper Semicontinuous Bonding Functions

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Abstract

We give several characterizations of inverse limits of compact metric spaces with upper semicontinuous set-valued bonding functions having the property that any closed subset of the inverse limit is the inverse limit of its projections. This solves a problem stated by Ingram.

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Acknowledgements

The authors wish to thank the anonymous referee for constructive remarks.

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Authors and Affiliations

  1. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000, Maribor, Slovenia

    Iztok Banič, Matevž Črepnjak, Matej Merhar & Uroš Milutinović

  2. Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000, Ljubljana, Slovenia

    Iztok Banič & Uroš Milutinović

  3. Andrej Marušič Institute, University of Primorska, Muzejski trg 2, 6000, Koper, Slovenia

    Iztok Banič & Matevž Črepnjak

  4. Faculty of Chemistry and Chemical Engineering, University of Maribor, Smetanova 17, 2000, Maribor, Slovenia

    Matevž Črepnjak

  5. Faculty of Civil Engineering, Transportation Engineering and Architecture, University of Maribor, Smetanova 17, 2000, Maribor, Slovenia

    Tina Sovič

Authors
  1. Iztok Banič
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  2. Matevž Črepnjak
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  3. Matej Merhar
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  4. Uroš Milutinović
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  5. Tina Sovič
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Corresponding author

Correspondence to Iztok Banič.

Additional information

Communicated by See Keong Lee.

This work is supported in part by the Slovenian Research Agency (research programs P1-0285 and P1-0297, and research projects J1-5433 and J1-7110).

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Banič, I., Črepnjak, M., Merhar, M. et al. The Closed Subset Theorem for Inverse Limits with Upper Semicontinuous Bonding Functions. Bull. Malays. Math. Sci. Soc. 42, 835–846 (2019). https://doi.org/10.1007/s40840-017-0517-5

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  • DOI: https://doi.org/10.1007/s40840-017-0517-5

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