Irreducibility of strong size levels

Abstract

Given a continuum X, Cn (X) denotes the hyperspace of nonempty closed subsets of X with at most n components. A strong size level is a subset of the form σ −1(t), where σ is a strong size map for Cn (X) and t ∈ (0, 1]. In this paper, answering a question by Capulín-Pérez, Fuentes-Montes de Oca, Lara-Mejía and Orozco-Zitli, we prove that for each n ≥ 2, no strong size level for Cn (X) is irreducible.