• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Doctoral Thesis
DOI
10.11606/T.45.2011.tde-23082011-225107
Document
Author
Full name
Ana Carolina Boero
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Tomita, Artur Hideyuki (President)
Alas, Ofelia Teresa
Ascui, Jorge Tulio Mujica
Kochloukov, Plamen Emilov
Pereira, Irene Castro
Title in Portuguese
Topologias enumeravelmente compactas em grupos abelianos de não torção via ultrafiltros seletivos
Keywords in Portuguese
compacidade enumerável
grupos topológicos
ultrafiltros seletivos
Abstract in Portuguese
Assumindo a existência de $\mathfrak c$ ultrafiltros seletivos dois a dois incomparáveis (segundo a ordem de Rudin-Keisler) provamos que o grupo abeliano livre de cardinalidade $\mathfrak c$ admite uma topologia de grupo enumeravelmente compacta com uma seqüência não trivial convergente. Sob as mesmas hipóteses, mostramos que um grupo topológico abeliano quase livre de torção $(G, +, \tau)$ com $|G| = |\tau| = \mathfrak c$ admite uma topologia independente de $\tau$ que o torna um grupo topológico e caracterizamos algebricamente os grupos abelianos de não torção que têm cardinalidade $\mathfrak c$ e que admitem uma topologia de grupo enumeravelmente compacta (sem seqüências não triviais convergentes). Provamos, ainda, que o grupo abeliano livre de cardinalidade $\mathfrak c$ admite uma topologia de grupo que torna seu quadrado enumeravelmente compacto e construímos um semigrupo de Wallace cujo quadrado é, também, enumeravelmente compacto. Por fim, assumindo a existência de $2^{\mathfrak c}$ ultrafiltros seletivos, garantimos que se um grupo abeliano de não torção e cardinalidade $\mathfrak c$ admite uma topologia de grupo enumeravelmente compacta, então o mesmo admite $2^{\mathfrak c}$ topologias de grupo enumeravelmente compactas (duas a duas não homeomorfas).
Title in English
Countably compact group topologies on non-torsion abelian groups from selective ultrafilters
Keywords in English
countable compactness
selective ultrafilters
topological groups
Abstract in English
Assuming the existence of $\mathfrak c$ pairwise incomparable selective ultrafilters (according to the Rudin-Keisler ordering) we prove that the free abelian group of cardinality $\mathfrak c$ admits a countably compact group topology that contains a non-trivial convergent sequence. Under the same hypothesis, we show that an abelian almost torsion-free topological group $(G, +, \tau)$ with $|G| = |\tau| = \mathfrak c$ admits a group topology independent of $\tau$ and we algebraically characterize the non-torsion abelian groups of cardinality $\mathfrak c$ which admit a countably compact group topology (without non-trivial convergent sequences). We also prove that the free abelian group of cardinality $\mathfrak c$ admits a group topology that makes its square countably compact and we construct a Wallace's semigroup whose square is countably compact. Finally, assuming the existence of $2^{\mathfrak c}$ selective ultrafilters, we ensure that if a non-torsion abelian group of cardinality $\mathfrak c$ admits a countably compact group topology, then it admits $2^{\mathfrak c}$ (pairwise non-homeomorphic) countably compact group topologies.
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
tese.pdf (990.54 Kbytes)
Publishing Date
2011-10-13
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
Centro de Informática de São Carlos
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2020. All rights reserved.