Geodesic
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 $.
Classification : 54A20, 54B10, 54C08
Keywords: sequentially continuous; sequentially complete; product space 
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     author = {Fri\v{c}, Roman and Kemoto, Nobuyuki},
     title = {Sequential completeness of subspaces of products of two cardinals},
     journal = {Czechoslovak Mathematical Journal},
     pages = {119--125},
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     zbl = {0949.54004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1999__49_1_a11/}
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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/