Induced mappings on symmetric products of continua

Given a continuum X and a positive integer n, let F-n(X) be the hyperspace of all nonempty subsets of X having at most n points. Given a mapping f : X -> Y between continua, we study the induced mapping f(n) : F-n(X) -> F-n(Y) given by f(n)(A) = f (A) (the image of A under f). In this paper, we prove some relationships among the mappings f and f(n) for the following classes of mappings: almost open, almost monotone, atriodic, feebly monotone, local homeomorphism, locally confluent, locally weakly confluent, strongly monotone and weakly semi confluent. (C) 2016 Elsevier B.V. All rights reserved.