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Transfinite large inductive dimensions modulo absolute Borel classes
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
Shimane University.
2009 (English)In: JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, ISSN 0025-5645 , Vol. 61, no 2, 327-344 p.Article in journal (Refereed) Published
Abstract [en]

The following inequalities between transfinite large inductive dimensions modulo absolutely additive (resp. multiplicative) Borel classes A(alpha) (resp. M(alpha)) hold in separable metrizable spaces:

(i) A(0)-trInd >= M(0)-trInd >= max{A(1)-trInd, M(1)-trInd}, and

(ii) min{A(alpha)-trInd, M(alpha)-trInd} >= max{A(beta)-trInd, M(beta)-trInd}, where 1 <= alpha < beta < omega(1).

We show that for any two functions a and m from the set of ordinals Omega = {alpha : alpha < omega(1)} to the set {-1} boolean OR Omega boolean OR {infinity} such that

(i) a(0) >= m(0) >= max{a(1), m(1)}, and

(ii) min{a(alpha), m(alpha)} >= max{a(beta), m(beta)}, whenever 1 <= alpha < beta < omega(1),

there is a separable metrizable space X such that A(alpha)-trInd X = a(alpha) and M(alpha)-trInd X = m(alpha) for each 0 <= alpha < omega(1).

Place, publisher, year, edition, pages
2009. Vol. 61, no 2, 327-344 p.
Keyword [en]
inductive dimensions modulo P, absolute Borel class, absolutely multipricative Borel class, absolutely additive Borel class, separable metrizable space
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-18271DOI: 10.2969/jmsj/06120327OAI: oai:DiVA.org:liu-18271DiVA: diva2:217842
Available from: 2009-05-16 Created: 2009-05-15 Last updated: 2009-05-16

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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf