On a question of de Groot and Nishiura (Q2773380)

The authors show the following, using some techniques developed for the construction of noncoinciding transfinite dimensions: Let \(n\leq 2^m - 1\) for some integer \(m\). Then, \(\text{cmp} Z_n \leq m + 1\). In particular, \(\text{cmp} Z_n <\text{def } Z_n\) for \(n \geq 5\), where \(Z_n\) is the space defined by de Groot and Nishiura, and they posed the following question:NEWLINENEWLINENEWLINEQuestion 1.1. Let \( Z_n = [0,1]^{n+1}\smallsetminus (0,1)^n \times \{0\}.\) Is it true that \(\text{cmp} Z_n\) for \(n\geq 3\)? NEWLINENEWLINENEWLINEThe authors answer this question for the cases \(n\geq 5\).