Ważewski's universal dendrite as an inverse limit with one set-valued bonding function | Zendy

Iztok Banič | Zendy; Matevž Črepnjak | Zendy; Matej Merhar | Zendy; Uroš Milutinović | Zendy; Tina Sovič | Zendy

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Ważewski's universal dendrite as an inverse limit with one set-valued bonding function

Author(s) -

Iztok Banič,

Matevž Črepnjak,

Matej Merhar,

Uroš Milutinović,

Tina Sovič

Publication year - 2013

Publication title -

glasnik matematicki

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.332

H-Index - 17

eISSN - 1846-7989

pISSN - 0017-095X

DOI - 10.3336/gm.48.1.12

Subject(s) - mathematics , inverse limit , limit (mathematics) , inverse , dendrite (mathematics) , set (abstract data type) , function (biology) , pure mathematics , mathematical analysis , discrete mathematics , geometry , computer science , evolutionary biology , biology , programming language

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\u27s 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

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