Induced mappings between quotient spaces of symmetric products of continua

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Abstract

Given a continuum X and n∈N. Let H(X)∈{2X,C(X),Fn(X)} be a hyperspace of X, where 2X, C(X) and Fn(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, SFmn(X) denotes the quotient space Fn(X)/Fm(X) and similarly, let SFmn(f) denote the natural induced mapping between SFmn(X) and SFmn(Y). In this paper we prove some relationships between the mappings f, 2f, C(f), Fn(f) and SFmn(f) for the following classes of mapping: atomic, confluent, light, monotone, open, OM, weakly confluent, hereditarily weakly confluent. © 2013 Elsevier B.V.

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Castañeda-Alvarado, E., Orozco-Zitli, F., & Sánchez-Martínez, J. (2014). Induced mappings between quotient spaces of symmetric products of continua. Topology and Its Applications, 163(1), 66–76. https://doi.org/10.1016/j.topol.2013.10.007

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