The Banach-Mazur game and products of Baire spaces

In this work we study Baire spaces and analyze the problem of product of Baire spaces. Then we present some conditions using the Banach-Mazur game to show that the Baire product is preserved in the product. Then we analyze the difference of the infinite product of Baire spaces, between the box produ...

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Detalles Bibliográficos
Autor: Medina, Gabriel Andre Asmat
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2020
País:Brasil
Institución:Universidade de São Paulo (USP)
Repositorio:Biblioteca Digital de Teses e Dissertações da USP
Idioma:inglés
OAI Identifier:oai:teses.usp.br:tde-10092020-171236
Acceso en línea:https://www.teses.usp.br/teses/disponiveis/55/55135/tde-10092020-171236/
Access Level:acceso abierto
Palabra clave:Baire spaces
Banach-Mazur game
Espaço de Baire
Jogo de Banach-Mazur
Jogos topológicos com multiplos tabuleiros
Multiboard topological games
Product of Baire spaces
Produto de espaços de Baire
Descripción
Sumario:In this work we study Baire spaces and analyze the problem of product of Baire spaces. Then we present some conditions using the Banach-Mazur game to show that the Baire product is preserved in the product. Then we analyze the difference of the infinite product of Baire spaces, between the box product and Tychonoff product. We also present a multiboard version for this problem. Finally we present some open problems regarding the product of Baire spaces.