Ważewski's universal dendrite as an inverse limit with one set-valued bonding function (Q2843836)

\textit{W. S. Mahavier} [Topology Appl. 141, No. 1--3, 225--231 (2004; Zbl 1078.54021)] introduced the study of inverse limits with set valued functions. For the particular case in which all the spaces are equal to the interval \([0,1]\) and all the functions coincide, the inverse limit can be defined as follows. Take a closed subset \(M\) in the unit square \([0,1] \times[0,1]\) such that both projections of \(M\) to \([0,1]\) are onto. Then \(lim_{\leftarrow} \mathbf{M}\) is defined as the set of sequences \((x_n)_n\) in the Hilbert cube such that \((x_{n+1},x_{n})\in M\) for each \(n\).NEWLINENEWLINEA fundamental question on this topic is: What spaces can be obtained as these types of inverse limits?NEWLINENEWLINEThis problem is very interesting even for the case of dendrites (locally connected continua without simple closed curves). One important step in this direction is the result of \textit{V. C. Nall} [Topology Appl. 159, No. 3, 733--736 (2012; Zbl 1242.54004)], who has shown that the arc is the only finite graph that can be obtained as such inverse limit.NEWLINENEWLINEIn the paper under review the authors show an appropriate closed subset \(M\) in \([0,1] \times[0,1]\) such that \(lim_{\leftarrow} \mathbf{M}\) is homeomorphic to the Ważewzki's universal dendrite.