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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2019.tde-18092019-163842
Document
Author
Full name
Matheus Duzi Ferreira Costa
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2019
Supervisor
Committee
Aurichi, Leandro Fiorini (President)
Dias, Rodrigo Roque
Ferreira, Carlos Henrique Grossi
Zdomskyy, Lyubomyr
Title in English
Topological games and selection principles
Keywords in English
Baire spaces
Covering properties
Selection principles
Tightness properties
Topological games
Abstract in English
This paper is dedicated to the beginning of the development of a book introducing topological games and selection principles. Here, the classical games (such as the Banach-Mazur) and selection principles (such as the Rothberger or Menger properties) are presented. The most notable applications are also displayed both the classical (such as the characterization of Baire spaces with the Banach-Mazur game) and the recent (such as the relation between the Menger property and D-spaces). In addition to the content for the book, a problem in finite combinatorics that was found in the study of positional strategies is presented (as well as a partial solution) together with some results regarding new variations of classical selection principles and games, which give rise to the characterization of some notable spaces.
Title in Portuguese
Jogos topológicos e princípios seletivos
Keywords in Portuguese
Espaços de Baire
Jogos topológicos
Princípios seletivos
Propriedades de coberturas
Propriedades de tightness
Abstract in Portuguese
Este trabalho é dedicado ao início do desenvolvimento de um livro introdutório à jogos topológicos e princípios seletivos. Aqui, são apresentados os clássicos jogos (tais como o de Banach-Mazur) e princípios seletivos (tais como a propriedade de Rothberger ou de Menger). Também são exibidas as aplicações mais notáveis encontradas na literatura tanto as mais tradicionais (tais como a caracterização de espaços de Baire com o jogo de Banach-Mazur), como as mais atuais (tais como a relação entre a propriedade de Menger e D-espaços). Além do conteúdo voltado para o livro, são apresentados um problema de combinatória finita (assim como uma solução parcial para tal) que foi encontrado com o estudo de estratégias posicionais e alguns resultados envolvendo novas variações de princípios de seleção e jogos clássicos, possibilitando a caracterização de alguns espaços notáveis.
 
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Publishing Date
2019-09-18
 
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