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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2021.tde-24052021-170942
Document
Author
Full name
Mariano Martin Rengifo Santander
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2021
Supervisor
Committee
Aurichi, Leandro Fiorini (President)
Dias, Rodrigo Roque
Junqueira, Lucia Renato
Silva, Samuel Gomes da
Title in Portuguese
Conjectura de Borel
Keywords in Portuguese
Medida nula forte
Propriedade de Rothberger
Abstract in Portuguese
A Conjectura de Borel diz que todo conjunto de números reais que tem medida nula forte é enumerável. Estendemos a noção de medida nula forte no contexto dos espaços métricos e dos espaços topológicos. Estudamos as relações entre a propriedade de Rothberger e a medida nula forte com alguns jogos topológicos. Mostramos as equivalências da Conjectura de Borel em termos dos jogos estudados.
Title in English
Borel's Conjecture
Keywords in English
Rothbergers property
Strong measure zero
Abstract in English
Borels Conjecture says that any set of real numbers that has strong measure zero is countable. We extend the notion of strong measure zero in the context of metric spaces and topological spaces. We studied the relations between the Rothbergers property and the strong measure zero with some topological games. We show the equivalences of Borels Conjecture in terms of the games studied.
 
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Publishing Date
2021-05-24
 
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