Superextension-type functors and soft mappings (Q760688)

Let \({\mathfrak B}\) be a class of bicompacta. The continuous mapping \(f: X\to Y\) is called ''\({\mathfrak B}\)-soft'' if for arbitrary \(Z\in {\mathfrak B}\), any closed subset \(A\subseteq Z\) and any continuous mappings \(H: Z\to Y\), \(g: A\to X\) such that \(fg=H|_ A\) there exists a mapping \(G: Z\to X\) with the properties \(G|_ A\) and \(fG=H\). The main result is Theorem 1. Here certain sufficient conditions are given under which the mapping \(\otimes Ff_ i\) is \({\mathfrak B}\)-soft for each finite family of mappings \(f_ i\). F denotes a covariant continuous functor preserving weight from the category of all bicompacta with surjective mappings to the same category.