Abstract

HERNANDEZ-VALDEZ, GERARDO; HERRERA-CARRASCO, DAVID; LOPEZ, MARÍA DE J.  and  MACIAS-ROMERO, FERNANDO. Properties of the (n, m)−fold hyperspace suspension of continua. Integración - UIS [online]. 2022, vol.40, n.2, pp.159-168.  Epub May 08, 2023. ISSN 0120-419X.  https://doi.org/10.18273/revint.v40n2-2022002.

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.

Keywords : Aposyndesis; Cantor manifold; Continuum; Colocal connected-ness; (n; m)−fold hyperspace suspension; Property (b); Unicoherent.

        · abstract in Spanish     · text in English     · English ( pdf )