The covering number and the transitive covering number may be totally different

Jan Kraszewski

doi:10.1023/b:amhu.0000045535.90334.dd

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Acta Mathematica Hungarica

Volume/Issue:: Volume 105: Issue 1-2

The covering number and the transitive covering number may be totally different

Author:

Jan Kraszewski

Jan Kraszewski
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Pages:: 115–119

Online Publication Date:: 11 Aug 2006

Publication Date:: 01 Oct 2004

Article Category:: Research Article

DOI:: https://doi.org/10.1023/b:amhu.0000045535.90334.dd

Keywords:: Abelian groups; ideals; covering number; Hamel basis

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Abstract

We construct a translation invariant σ-ideal T(κ) (where κ is an infinite cardinal number) such that cov_t (T(κ)) = 2^κ while cov (T(κ)) = cof (T(κ)) = ω₁. The constructions can be carried out in R as well.

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Acta Mathematica Hungarica

Print ISSN:: 0236-5294

Online ISSN:: 1588-2632

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Acta Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1950
Volumes per Year	3
Issues per Year	6
Founder	Magyar Tudományos Akadémia
Founder's Address	H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0236-5294 (Print)
ISSN	1588-2632 (Online)