Induced mappings on symmetric products, some answers.

Given a continuum X , let F n ( X ) denote the hyperspace of nonempty subsets of X with at most n points. For n ≥ 2 , let S F n ( X ) = F n ( X ) / F 1 ( X ) be the quotient space. Given a mapping between continua f : X → Y , we consider the induced mappings f n : F n ( X ) → F n ( Y ) and S f n : S F n ( X ) → S F n ( Y ) . Given a class of mappings M , in this paper we consider relations between the statements f ∈ M , f n ∈ M and S f n ∈ M , and we answer some questions about these relations considering the following classes of mappings: almost monotone, atriodic, freely decomposable and joining. [ABSTRACT FROM AUTHOR]