Abstract:We study closed subspaces of $\kappa$-Ohio complete spaces and, for $\kappa$ uncountable cardinal, we prove a characterization for them. We then investigate the behaviour of products of $\kappa$-Ohio complete spaces. We prove that, if the cardinal $\kappa^+$ is endowed with either the order or the discrete topology, the space $(\kappa^+)^{\kappa^+}$ is not $\