Factorization of mappings of topological spaces and homomorphisms of topological groups in accordance with weight and dimension \(\text{ind}\) (Q1910262)

Given a continuous mapping \(f : X \to Y\) of a compact space \(X\) to \(Y\), there exist a compact space \(Z\) and continuous mappings \(g : X \to Z\) and \(h : Z \to Y\) such that \(f = h \circ g\), \(Z = g(X)\), \(w(Z) \leq w (Y)\) and \(\dim Z \leq \dim Y\). This factorization theorem of Mardešić is also valid for the large inductive dimension Ind (B. A. Pasynkov) and for the small inductive dimension ind (I. M. Leibo). The author proves certain analogues of the Mardešić factorization theorem for the dimension ind. He shows in particular that all continuous mappings of hereditarily Lindelöf spaces can be factorized in accordance with the weight and the small inductive dimension. A similar assertion is valid for continuous homomorphisms of hereditarily Lindelöf topological groups (and of Lindelöf \(\Sigma\)-groups, too).