Countably compact groups, selective ultrafilters and forcing
Aspects of weakenings of normality, compactness and infinitary combinatorics in to...
Topological and paratopological groups and countable compactness
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Countably compact group topologies: MA, forcing and selective ultrafilters
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| Author(s): |
Jury Fabiana Castiblanco Quiroga
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2011-11-07 |
| Examining board members: |
Artur Hideyuki Tomita;
Christina Brech;
Irene Castro Pereira
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| Advisor: | Artur Hideyuki Tomita |
| Abstract | |
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. (AU) | |
| FAPESP's process: | 09/03768-1 - Countably compact groups, selective ultrafilters and forcing |
| Grantee: | Jury Fabiana Castiblanco Quiroga |
| Support Opportunities: | Scholarships in Brazil - Master |