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Keywords:
$\kappa$-Ohio complete; compactification; subspace; product
$\kappa$-Ohio complete; compactification; subspace; product
Summary:
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 $\kappa$-Ohio complete. As a consequence, we show that, if $\kappa$ is less than the first weakly inaccessible cardinal, then neither the space $\omega^{\kappa^+}$, nor the space $\mathbb{R}^{\kappa^+}$ is $\kappa$-Ohio complete.
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