An \(n\)-cell as a generalized inverse limit indexed by the integers (Q2134979)

\textit{W. T. Ingram} and \textit{W. S. Mahavier} [Houston J. Math. 32, No. 1, 119--130 (2006; Zbl 1101.54015)] introduced inverse limits of inverse sequences of compact metric spaces with upper semicontinuous bonding functions, which present a generalization of inverse limits of inverse sequences of compact metric spaces with continuous bonding functions. In this generalization it is assumed that an inverse sequence is indexed by positive integers. Since the generalization was introduced, many authors have been interested in this research field and many papers have appeared. Among other things, it was proven that a \(2\)-cell could not be obtained as an inverse limit of closed unit intervals with one upper semicontinuous bonding function. Later a new generalization of generalized inverse limits appeared where all spaces and all upper semicontinuous bonding functions are indexed by integers. The usefulness of these inverse limits is demonstrated by the result that says that a 2-cell can be obtained as an inverse limit of closed unit intervals with one set-valued bonding function indexed by the integers. In the present article, we find a more general result: an arbitrary \(n\)-cell can be obtained as an inverse limit of an inverse sequence of closed unit intervals with one bonding function (indexed by the integers). This also answers a question by \textit{R. P. Vernon} [Topology Appl. 171, 35--40 (2014; Zbl 1297.54044)]. Thus, this result shows that we get a new technique to obtain spaces with desired properties.