# Sequential completeness of subspaces of products of two cardinals

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

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## Abstract

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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 ${\left({\omega }_{1}+1\right)}^{2}$ need not be sequentially complete, but note that $X=A×B$ is sequentially complete whenever $A$ and $B$ are subspaces of $\kappa$.

## How to cite

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Frič, 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
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 -

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