Gowda, M. Seetharama; Sznajder, Roman Weak univalence and connectedness of inverse images of continuous functions. (English) Zbl 0977.90060 Math. Oper. Res. 24, No. 1, 255-261 (1999). Summary: A continuous function \(f\) with domain \(X\) and range \(f(X)\) in \(R^n\) is weakly univalent if there is a sequence of continuous one-to-one functions on \(X\) converging to \(f\) uniformly on bounded subsets of \(X\). In this article, we establish, under certain conditions, the connectedness of an inverse image \(f^{-1}(q)\). The univalence results of Radulescu-Radulescu, Moré-Rheinboldt, and Gale-Nikaido follow from our main result. We also show that the solution set of a nonlinear complementarity problem corresponding to a continuous \(P_0\)-function is connected if it contains a nonempty bounded clopen set; in particular, the problem will have a unique solution if it has a locally unique solution. Cited in 20 Documents MSC: 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) Keywords:weak univalence; connectedness; complementarity problem PDFBibTeX XMLCite \textit{M. S. Gowda} and \textit{R. Sznajder}, Math. Oper. Res. 24, No. 1, 255--261 (1999; Zbl 0977.90060) Full Text: DOI Link