Induced mappings between quotient spaces of symmetric products of continua

摘要

Given a continuum X and n ∈ N. Let H(X) ∈ {2~X,C(X), F_n(X)} be a hyperspace of X, where 2~X, C(X) and F_n(X) are the hyperspaces of all nonempty closed subsets of X, all subcontinua of X and all nonempty subsets of X with at most n points, respectively, with the Hausdorff metric. For a mapping f : X→Y between continua, let H(f) : H(X)→H(Y) be the induced mapping by f, given by H(f)(A) = f(A). On the other hand, for 1 ≤m≤n, SF_m~n(X) denotes the quotient space F_n(X)/F_m(X) and similarly, let SF_m~n(f) denote the natural induced mapping between SF_m~n(X) and SF_m~n(Y). In this paper we prove some relationships between the mappings f, 2~f, C(f), F_n(f) and SF_m~n(f) for the following classes of mapping: atomic, confluent, light, monotone, open, OM, weakly confluent, hereditarily weakly confluent.