Induced mappings on symmetric products of continua

Given a continuum X and a positive integer n  , let Fn(X)Fn(X) be the hyperspace of all nonempty subsets of X having at most n   points. Given a mapping f:X→Yf:X→Y between continua, we study the induced mapping fn:Fn(X)→Fn(Y)fn:Fn(X)→Fn(Y) given by fn(A)=f(A)fn(A)=f(A) (the image of A under f). In this paper, we prove some relationships among the mappings f   and fnfn 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.