Weak Univalence and Connectedness of Inverse Images of Continuous Functions

Authors:
M. Seetharama Gowda;Roman Sznajder
Affiliations:
-;-
Venue:
Mathematics of Operations Research
Year:
1999

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Abstract

A continuous function f with domain X and range f(X) in Rn 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, More-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 P0-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.