Abstract. We construct a family of upper semi-continuous setvalued 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.
We investigate inverse limits in the category CHU of compact Hausdorff spaces with upper semicontinuous functions. We introduce the notion of weak inverse limits in this category and show that the inverse limits with upper semicontinuous set-valued bonding functions (as they were defined by Ingram and Mahavier ['Inverse limits of upper semi-continuous set valued functions', Houston J. Math. 32 (2006), 119-130]) together with the projections are not necessarily inverse limits in CHU but they are always weak inverse limits in this category. This is a realisation of our categorical approach to solving a problem stated by Ingram [An Introduction to Inverse Limits with Set-Valued Functions (Springer, New York, 2012)].
Podnaslov: Skripta Avtorja: asist. dr. Tina Sovič (Univerza v Mariboru, Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo) izr. prof. dr. Simon Špacapan (Univerza v Mariboru, Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo) Recenzenta: red. prof. dr. Borut Zalar (Univerza v Mariboru, Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo) doc. dr. Rija Erveš (Univerza v Mariboru, Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo) Grafične priloge: Avtorja Tehnični urednik: doc. dr. Andrej Tibaut (Univerza v Mariboru, Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo)
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