2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69437We give an elementary proof of a monotone selection principle which allows to pass from increasing nets to increasing sequences in the Hermitian part of a $σ$-finite von Neumann algebra. This is to be seen as a ``monotone version'' of first countability.Functional AnalysisOperator Algebras46L10; 28C05text