On topological classification of complex mappings
We study the topological invariant $\phi $ of Kwieciński and Tworzewski, particularly beyond the case of mappings with smooth targets. We derive a lower bound for $\phi $ of a general mapping, which is similarly effective as the upper bound given by Kwieciński and Tworzewski. Some classes of mappings are identified for which the exact value of $\phi $ can be computed. Also, we prove that the variation of $\phi $ on the source space of a mapping with a smooth target is semicontinuous in the Zariski topology.