Abstract
Let κ be a cardinal number with the usual order topology. We prove that all subspaces of κ2 are weakly sequentially complete and, as a corollary, all subspaces of \(\omega _1^2 \) are sequentially complete. Moreover we show that a subspace of (ω1 + 1)2 need not be sequentially complete, but note that X = A × B is sequentially complete whenever A and B are subspaces of κ.
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Frič, R., Kemoto, N. Sequential completeness of subspaces of products of two cardinals. Czechoslovak Mathematical Journal 49, 119–125 (1999). https://doi.org/10.1023/A:1022464326296
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DOI: https://doi.org/10.1023/A:1022464326296