2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68158We study the omega-limit sets $ω_X(x)$ in an isolating block $U$ of a singular-hyperbolic attractor for three-dimensional vector fields $X$. We prove that for every vector field $Y$ close to $X$ the set $ \{x\in U:ω_Y(x)$ contains a singularity$\}$ is {\em residual} in $U$. This is used to prove the persistence of singular-hyperbolic attractors with only one singularity as chain-transitive Lyapunov stable sets. These results generalize well known properties of the geometric Lorenz attractor \cite{gw} and the example in \cite{mpu}.17 pagesDynamical SystemsPrimary 37D30, Secondary 37B25text