The number of non-solutions to an equation in a group and non-topologizable torsion-free groups

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97060It is shown that, for any pair of cardinals with infinite sum, there exist a group and an equation over this group such that the first cardinal is the number of solutions to this equation and the second cardinal is the number of non-solutions to this equation. A countable torsion-free non-topologizable group is constructed.5 pages; minor changes in the introduction and referencesGroup TheoryGeneral Topology20F05, 20F06, 22A05, 54H11The number of non-solutions to an equation in a group and non-topologizable torsion-free groupstext