On the topology of n-valued maps

Abstract

This paper presents an exposition of the topological foundations of the theory of n-valued maps. By means of proofs that exploit particular features of n-valued functions, as distinct from more general classes of multivalued functions, we establish, among other properties, the equivalence of several definitions of continuity. The exposition includes an exploration of the role of configuration spaces in the study of n-valued maps. As a consequence of this point of view, we extend the classical Splitting Lemma, that is central to the fixed point theory of n-valued maps, to a characterization theorem that leads to a new type of construction of non-split n-valued maps.