Geodesic
More on $\kappa$-Ohio completeness
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 551-559.

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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.
Classification : 54B05, 54B10, 54D35
Keywords: $\kappa$-Ohio complete; compactification; subspace; product 
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     author = {Basile, D.},
     title = {More on $\kappa${-Ohio} completeness},
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Basile, D. More on $\kappa$-Ohio completeness. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 551-559. http://geodesic.mathdoc.fr/item/CMUC_2011__52_4_a6/