Glasnik Matematicki, Vol. 59, No. 1 (2024), 193-212. \( \)

MARKOV SET-VALUED FUNCTIONS ON COMPACT METRIC SPACES

Iztok Banič, Matevž Črepnjak and Teja Kac

(1) Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, SI-2000 Maribor, Slovenia, (2) Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia, (3) Andrej Marušič Institute, University of Primorska, Muzejski trg 2, SI-6000 Koper, Slovenia
e-mail:iztok.banic@um.si

(1) Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, SI-2000 Maribor, Slovenia, (2) Faculty of Chemistry and Chemical Engineering, University of Maribor, Smetanova 17, SI-2000 Maribor, Slovenia
e-mail:matevz.crepnjak@um.si

Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, SI-2000 Maribor, Slovenia
e-mail:teja.kac1@um.si

Abstract.   We generalize the notion of Markov functions on closed intervals \([a,b]\) to Markov set-valued functions on compact metric spaces. We also introduce when two such Markov set-valued functions follow the same pattern and show that if the Markov set-valued functions \(F:X\multimap X\) and \(G:Y\multimap Y\) follow the same pattern, then the inverse limits \(\lim_{{\multimap}}(X,F)\) and \(\lim_{\multimap}(Y,G)\) are homeomorphic.

2020 Mathematics Subject Classification.   54F17, 54C60, 54E45

Key words and phrases.   Markov set-valued function, inverse limit, upper semicontinuos function, compact metric space

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https://doi.org/10.3336/gm.59.1.09

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