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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2011.tde-07092012-163026
Document
Author
Full name
Jury Fabiana Castiblanco Quiroga
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Tomita, Artur Hideyuki (President)
Brech, Christina
Pereira, Irene Castro
Title in Portuguese
Topologias de grupo enumeravelmente compactas: MA, forcing e ultrafiltros seletivos
Keywords in Portuguese
Axioma de Martin
compacidade enumerável
Forcing
grupo topológico
ultrafiltro seletivo
Abstract in Portuguese
É bem conhecido o fato de que todo grupo compacto tem sequências não triviais convergentes. A existência de grupos enumeravelmente compactos sem sequências não triviais convergentes, foi provada usando axiomas adicionais à axiomática usual ZFC: A. Hajnal e I. Juhász sob CH, E. K. van Douwen sob MA, A. H. Tomita sob MA(sigma-centrada) e R.E. Madariaga-Garcia e A. H. Tomita usando ultrafiltros seletivos. Neste trabalho, estudaremos algumas construções recentes relacionadas com as citadas acima, usando o Axioma de Martin, ultrafiltros seletivos e forcing. Essas construções estão relacionadas com algumas questões indicadas por A.D. Wallace, E. van Douwen, M. Tkachenko, D. Dikranjan e D. Shakhmatov
Title in English
Countably compact group topologies: MA, forcing and selective ultrafilters
Keywords in English
countable compactness
Forcing
Martin Axiom
selective ultrafilter.
topological group
Abstract in English
It is well known that every compact group has non-trivial convergent sequences. The existence of countably compact groups without non-trivial convergent sequences was proved using extra set-theoretical assumptions: A. Hajnal and I. Juhasz under CH, E. K. van Douwen under MA, A.H.Tomita under MA(centered) and R.E.Madariaga-Garcia and A.H. Tomita using a selective ultrafilter. I n this work, we study some recent constructions related to the ones given above using Martin Axiom, selective ultrafilters and forcing, related to questions raised by A.D. Wallace, E. van Douwen, M. Tkacenko, D. Dikranjan and D. Shakhmatov.
 
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dissertacao_fabi.pdf (1.45 Mbytes)
Publishing Date
2012-09-10
 
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