1. Sequential completeness of subspaces of products of two cardinals
- Creator:
- Frič, Roman and Kemoto, Nobuyuki
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- sequentially continuous, sequentially complete, and product space
- Language:
- English
- Description:
- 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 $.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public