Sequential decreasing strong size properties

Abstract

Abstract Let 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, { t j } 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.