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Title: Sequential completeness of subspaces of products of two cardinals (English)
Author: Frič, Roman
Author: Kemoto, Nobuyuki
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 49
Issue: 1
Year: 1999
Pages: 119-125
Summary lang: English
Category: math
Summary: 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 $. (English)
Keyword: sequentially continuous
Keyword: sequentially complete
Keyword: product space
MSC: 54A20
MSC: 54B10
MSC: 54C08
idZBL: Zbl 0949.54004
idMR: MR1676829
Date available: 2009-09-24T10:20:34Z
Last updated: 2020-07-03
Stable URL:
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Reference: [KOT] N. Kemoto, H. Ohta and K. Tamano: Products of spaces of ordinal numbers.Top. Appl. 45 (1992), 245–260. MR 1180812
Reference: [No] J. Novák: On sequential envelope.In General Topology and its Relations to Modern Analysis and Algebra I (Proc. First Prague Topological Sympos., 1961 ), Publishing House of the Czecoslovak Academy of Sciences, Praha, 1962, pp. 292–294. MR 0175082


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