Darboux transformations (Q1100575)

Let X and Y be topological spaces. The author considers Darboux transformations, i.e. mappings \(f: X\to Y\) such that f(L) is connected for every arc \(L\subset X\). He states without proofs a series of results belonging to the following subjects: generalization for mappings \(f: {\mathbb{R}}^ 2\to {\mathbb{R}}^ 2\) of Zahorski's theory of Darboux Baire 1 functions [\textit{Z. Zahorski}, Trans. Am. Math. Soc. 69, 1-54 (1950; Zbl 0038.206)]; Darboux transformations \(f: {\mathbb{R}}^ 2\to {\mathbb{R}}^ 2\) of bounded variation; extensions of Darboux transformations; characterization of Darboux transformations by local properties.