Glasnik Matematicki, Vol. 48, No. 1 (2013), 137-165.

WAŻEWSKI'S UNIVERSAL DENDRITE AS AN INVERSE LIMIT WITH ONE SET-VALUED BONDING FUNCTION

Iztok Banič, Matevž Črepnjak, Matej Merhar, Uroš Milutinović and Tina Sovič

Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, Maribor 2000, Slovenia, and, Institute of Mathematics, Physics and Mechanics, Jadranska 19, Ljubljana 1000, Slovenia
e-mail: iztok.banic@uni-mb.si

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

Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, Maribor 2000, Slovenia
e-mail: matej.merhar@uni-mb.si

Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, Maribor 2000, Slovenia, and, Institute of Mathematics, Physics and Mechanics, Jadranska 19, Ljubljana 1000, Slovenia
e-mail: uros.milutinovic@uni-mb.si

Faculty of Civil Engineering, University of Maribor, Smetanova 17, Maribor 2000, Slovenia
e-mail: tina.sovic@um.si


Abstract.   We construct a family of upper semi-continuous set-valued functions f:[0,1] → 2[0,1] (belonging to the class of so-called comb functions), such that for each of them the inverse limit of the inverse sequence of intervals [0,1] and f as the only bonding function is homeomorphic to Ważewski's universal dendrite. Among other results we also present a complete characterization of comb functions for which the inverse limits of the above type are dendrites.

2010 Mathematics Subject Classification.   54F50, 54C60.

Key words and phrases.   Continua, inverse limits, upper semi-continuous functions, dendrites, Ważewski's universal dendrite.


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DOI: 10.3336/gm.48.1.12


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