Stably essential mappings onto disks (Q1307386)

From the authors abstract: ``Let \(f\) be an essential mapping from a compact metric space \(X\) onto the \(n\)-dimensional disk \(D^n\) and let \(n \leq 2\) or \(\dim X < 2n - 2\). It is known that \(f\) is stably essential, i.e. the product mapping \(f \times id_{I^k}\) of \(f\) and the identity mapping \(id_{I^k}\) on the \(k\)-dimensional cube \(I^k\) is essential for all \(k\). In this paper it is shown that the \(m\)-fold cone mapping \(C_m(f) : C_m(X) \to D^{m+n}\) and the \(m\)-fold suspension mapping \(S_m(f) : S_m(X) \to D^{m+n}\) are stably essential for any \(m\). It is also established that under the assumption mentioned above the mappings \(f \times id_{I^m}\), \(C_m(f)\) and \(S_m(f)\) are all coincidence universal for any \(m\)''.