Weak Univalence and Connectedness of Inverse Images of Continuous Functions
- 1 February 1999
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research
- Vol. 24 (1) , 255-261
- https://doi.org/10.1287/moor.24.1.255
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, 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 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.Keywords
This publication has 13 references indexed in Scilit: