2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100008Let a finite non-empty X is equipped with discrete topology. We prove that S \subseteq X^ωis of second category if and only if for each f:ω-> \bigcup_{n \in ω} X^n there exists a sequence {a_n}_{n \in ω} belonging to S such that for infinitely many i \in ωthe infinite sequence {a_{i+n}}_{n \in ω} extends the finite sequence f(i).with a counterexample by T. Bartoszynski, to appear in J. Nat. GeomLogicMathematical PhysicsGeneral Topology03E05 (Primary), 54E52 (Primary)text