HERNANDEZ-VALDEZ, GERARDO; HERRERA-CARRASCO, DAVID; LOPEZ, MARÍA DE J.    MACIAS-ROMERO, FERNANDO. Properties of the (n, m)−fold hyperspace suspension of continua. []. , 40, 2, pp.159-168.   08--2023. ISSN 0120-419X.  https://doi.org/10.18273/revint.v40n2-2022002.

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Let n, m ∈ N with m ≤ n and X be a metric continuum. We con-sider the hyperspaces C n (X) (respectively, F n (X)) of all nonempty closed subsets of X with at most n components (respectively, n points). The (n, m)−fold hyperspace suspension on X was introduced in 2018 by Anaya, Maya, and Vázquez-Juárez, to be the quotient space C n (X)/F m (X) which is obtained from C n (X) by identifying F m (X) into a one-point set. In this paper we prove that C n (X)/F m (X) contains an n−cell; C n (X)/F m (X) has prop-erty (b); C n (X)/F m (X) is unicoherent; C n (X)/F m (X) is colocally connected; C n (X)/F m (X) is aposyndetic; and C n (X)/F m (X) is finitely aposyndetic.

Sean n, m ∈ N con m ≤ n y X un continuo métrico. Conside-ramos el hiperespacio de todos los subconjuntos cerrados, no vacíos de X con a lo más n componentes (respectivamente, n puntos) C n (X) (respecti-vamente, F n (X)). El (n, m)−ésimo hiperespacio suspensión de X lo intro-dujeron, en 2018, Anaya, Maya y Vázquez-Juárez, como el espacio cociente C n (X)/F m (X) que se obtiene de C n (X) al identificar F m (X) a un conjunto de un punto. En este artículo demostramos que C n (X)/F m (X) contiene una n−celda; C n (X)/F m (X) tiene la propiedad (b); C n (X)/F m (X) es unicohe-rente; C n (X)/F m (X) es colocalmente conexo; C n (X)/F m (X) es aposindético y C n (X)/F m (X) es finitamente aposindético.

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