Cones and suspensions that are Hilbert cubes (Q1275308)

For a space \(Y\), let \(\text{Cone}(Y)\) and \(\Sigma(Y)\) be the cone over \(Y\) and the suspension over \(Y\). This article shows that if any one of \(\text{Cone}(Y)\), \(\Sigma(Y)\), and \(Y\times [0,1]\) is homeomorphic to the Hilbert cube, \(Q\), then they all are. When \(Y\) is a \(Q\)-manifold, this only happens when \(Y\) itself is homeomorphic to \(Q\). However, an example is given of a non-\(Q\)-manifold \(Y\) where this also happens. In addition, \(\text{Cone}(Y)\) and \(\Sigma(Y)\) are compact \(Q\)-manifolds only if they are homeomorphic to \(Q\).