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Sequential completeness of subspaces of products of two cardinals
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 1, pp. 119-125
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Let $\kappa $ be a cardinal number with the usual order topology. We prove that all subspaces of $\kappa ^2$ are weakly sequentially complete and, as a corollary, all subspaces of $\omega _1^2$ are sequentially complete. Moreover we show that a subspace of $(\omega _1+1)^2$ need not be sequentially complete, but note that $X=A\times B$ is sequentially complete whenever $A$ and $B$ are subspaces of $\kappa $.
Let $\kappa $ be a cardinal number with the usual order topology. We prove that all subspaces of $\kappa ^2$ are weakly sequentially complete and, as a corollary, all subspaces of $\omega _1^2$ are sequentially complete. Moreover we show that a subspace of $(\omega _1+1)^2$ need not be sequentially complete, but note that $X=A\times B$ is sequentially complete whenever $A$ and $B$ are subspaces of $\kappa $.
Classification : 54A20, 54B10, 54C08
Keywords: sequentially continuous; sequentially complete; product space 
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}
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Frič, Roman; Kemoto, Nobuyuki. Sequential completeness of subspaces of products of two cardinals. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 1, pp. 119-125. http://geodesic.mathdoc.fr/item/CMJ_1999_49_1_a11/

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