2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102231We show there is no categorical metric continuum. This means that for every metric continuum X there is another metric continuum Y such that X and Y have (countable) elementarily equivalent bases but X and Y are not homeomorphic. As an application we show that the chainability of the pseudoarc is not a first-order property of its lattice of closed sets.Revision after comments from referee (2006-01-16)General TopologyLogic54F12 (Primary); 03C20, 03C35, 54F50 (Secondary)text