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Map** Theorems for Inverse Limits with Set-Valued Bonding Functions

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Abstract

We revisit the results from two papers, Mioduszewski’s “Map**s of inverse limits” and Feuerbacher’s “Map**s of inverse limits revisited” to obtain new map** theorems for inverse limits of inverse sequences of compact metric spaces with continuous single-valued bonding functions. Then, we apply the results to the theory of inverse limits of inverse sequences of compact metric spaces with upper semicontinuous set-valued bonding functions to obtain new map** theorems for such inverse limits. This answers an open problem stated by Ingram.

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Notes

  1. The definition of a polyhedron may be found in [3, pp. 470–473].

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Acknowledgements

The authors thank the anonymous referee for careful reading and constructive remarks that helped us improve the paper.

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Authors and Affiliations

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

    Iztok Banič

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

    Iztok Banič

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

    Iztok Banič

  4. Department of Mathematics, Faculty of Science, University of Split, Rudera Boškovića 33, Split, Croatia

    Goran Erceg

  5. Lamar University, 200 Lucas Building, P.O. Box 10047, Beaumont, TX, 77710, USA

    Judy Kennedy

Authors
  1. Iztok Banič
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  2. Goran Erceg
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  3. Judy Kennedy
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Correspondence to Iztok Banič.

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Communicated by Rosihan M. Ali.

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This work is supported in part by the Slovenian Research Agency (research program P1-0285).

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Banič, I., Erceg, G. & Kennedy, J. Map** Theorems for Inverse Limits with Set-Valued Bonding Functions. Bull. Malays. Math. Sci. Soc. 45, 2905–2940 (2022). https://doi.org/10.1007/s40840-022-01307-y

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  • DOI: https://doi.org/10.1007/s40840-022-01307-y

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