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Doctoral Thesis
DOI
10.11606/T.45.2012.tde-08112012-001644
Document
Author
Full name
Rodrigo Roque Dias
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Junqueira, Lucia Renato (President)
Alas, Ofelia Teresa
Carnielli, Walter Alexandre
Passos, Marcelo Dias
Silva, Samuel Gomes da
Title in Portuguese
Princípios de seleção, jogos topológicos e indestrutibilidade de espaços compactos
Keywords in Portuguese
espaços D-separáveis
espaços de Lindelöf indestrutíveis
jogos topológicos
princípios de seleção
Abstract in Portuguese
Este trabalho se dedica ao estudo da interação entre princípios de seleção e jogos topológicos. Isto inclui uma abordagem não-topológica destes tópicos, com aplicações à indestrutibilidade de espaços de Lindelöf e a uma versão seletiva de d-separabilidade, dentre outros. Provamos ainda a não-equivalência consistente entre indestrutibilidade e o princípio de seleção naturalmente associado a esta propriedade, o que conduz à investigação da indestrutibilidade de espaços compactos. Finalmente, mostramos que algumas afirmações que limitam a cardinalidade de espaços de Lindelöf indestrutíveis são equiconsistentes com a existência de certos tipos de grandes cardinais.
Title in English
Selection principles, topological games and indestructibility of compact spaces
Keywords in English
D-separable spaces
indestructible Lindelöf spaces
selection principles
topological games
Abstract in English
In the present work we focus on the interplay between selection principles and topological games. This includes a nontopological approach to these topics, with applications to indestructibility of Lindelöf spaces and a selective version of d-separability, among others. We also show the consistent nonequivalence between indestructibility and the selection principle naturally associated to it, which leads to an investigation of indestructibility of compact spaces. We conclude by showing that some constraints on the cardinality of Lindelöf indestructible spaces are equiconsistent with the existence of some kinds of large cardinals.
 
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tesefinal.pdf (775.69 Kbytes)
Publishing Date
2012-11-08
 
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