# Sequential completeness of subspaces of products of two cardinals

Czechoslovak Mathematical Journal (1999)

- Volume: 49, Issue: 1, page 119-125
- ISSN: 0011-4642

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topFrič, Roman, and Kemoto, Nobuyuki. "Sequential completeness of subspaces of products of two cardinals." Czechoslovak Mathematical Journal 49.1 (1999): 119-125. <http://eudml.org/doc/30470>.

@article{Frič1999,

abstract = {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 $.},

author = {Frič, Roman, Kemoto, Nobuyuki},

journal = {Czechoslovak Mathematical Journal},

keywords = {sequentially continuous; sequentially complete; product space; sequentially continuous; sequentially complete; product space},

language = {eng},

number = {1},

pages = {119-125},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Sequential completeness of subspaces of products of two cardinals},

url = {http://eudml.org/doc/30470},

volume = {49},

year = {1999},

}

TY - JOUR

AU - Frič, Roman

AU - Kemoto, Nobuyuki

TI - Sequential completeness of subspaces of products of two cardinals

JO - Czechoslovak Mathematical Journal

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 49

IS - 1

SP - 119

EP - 125

AB - 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 $.

LA - eng

KW - sequentially continuous; sequentially complete; product space; sequentially continuous; sequentially complete; product space

UR - http://eudml.org/doc/30470

ER -

## References

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