TY - JOUR
AU - Illanes, Alejandro
AU - Martínez-de-la-Vega, Verónica
PY - 2022/10/03
Y2 - 2024/10/14
TI - Dynamics of induced mappings on symmetric products, some answers
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 23
IS - 2
SE -
DO - 10.4995/agt.2022.17492
UR - https://polipapers.upv.es/index.php/AGT/article/view/17492
SP - 235-242
AB - <p>Let X be a metric continuum and n a positive integer. Let F<sub>n</sub> (X) be the hyperspace of nonempty subsets of X with at most n points. If 0 < m < n, we consider the quotient space F<sup>n</sup><sub>m</sub> (X) = F<sub>n</sub> (X)/F<sub>m</sub> (X). Given a mapping f from X into X, we consider the induced mappings f<sub>n</sub> from F<sub>n</sub> (X) into F<sub>n</sub> (X) and f<sup>n</sup><sub>m</sub> from F<sup>n</sup><sub>m</sub> (X) into F<sup>n</sup><sub>m</sub> (X). In this paper we study the relations among the dynamics of the mappings f, f<sub>n</sub>, and f<sup>n</sup><sub>m</sub> and we answer some questions, by F. Barragán, A. Santiago-Santos and J. Tenorio, related to the properties: minimality, irreducibility, strong transitive and turbulence.</p>
ER -