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AbstractLet X be a continuum. The n-fold hyperspace Cn(X), n < ∞, is the space of all nonempty closed subsets of X with at most n components. A topological property P$ \mathcal{P} $ is said to be a (an almost) sequential decreasing strong size property provided that if μ is a strong size map for Cn(X, {tj}j=1∞$ \{t_{j}\}_{j=1}^{\infty} $ is a sequence in the interval (t,1) such that lim tj = t ∈ [0,1) (t ∈ (0,1)) and each fiber μ−1(tj) has property P$ \mathcal{P} $, then so does μ−1(t). In this paper we show that the following properties are sequential decreasing strong size properties: being a Kelley continuum, local connectedness, continuum chainability and, unicoherence. Also we prove that indecomposability is an almost sequential decreasing strong size property.
Mathematica Slovaca – de Gruyter
Published: Oct 25, 2018
Keywords: Primary 54C05, 54C10, 54B20; Secondary 54B15; n -fold hyperspace; strong size property; strong size map; Kelley continuum; indecomposability; local connectedness; continuum chainability and unicoherence
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