Covering properties,reflections in elementary submodels and partitions on topological spaces
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da USP |
Texto Completo: | https://doi.org/10.11606/T.45.2022.tde-12102022-112918 |
Resumo: | This work develops two distinct topics. We first work with partitions on topological spaces, developing some topics found on [27]. We fixed the proof of the first theorem from the previous paper. We also improved the consistency of a result obtained using by constructing an example consistent with ¬. In relation with the second topic we studied the spaces developed on [25]. For this we followed the line of work of the thesis [16]. We see that, for scattered spaces the properties Rothberger, Menger and indestructibly Lindelöf are preserved for elementary submodels. Furthermore we continue to investigate these preservations for more general spaces. Finally we worked with spaces and elementary submodels. |
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info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis Covering properties,reflections in elementary submodels and partitions on topological spaces Propriedades de cobertura, reflexões em submodelos elementares e partições em espaços topológicos 2022-08-19Lucia Renato JunqueiraRodrigo Roque DiasGabriel Zanetti Nunes FernandesRenan Maneli MezabarbaMarcelo Dias PassosRodrigo Rey CarvalhoUniversidade de São PauloMatemáticaUSPBR Covering properties Elementary submodels Espaços de funções Forcing Forcing Function spaces Partição de espaços topológicos Propriedades de cobertura Ramsey theory Submodelos elementares Teoria de Ramsey Topological space partitions This work develops two distinct topics. We first work with partitions on topological spaces, developing some topics found on [27]. We fixed the proof of the first theorem from the previous paper. We also improved the consistency of a result obtained using by constructing an example consistent with ¬. In relation with the second topic we studied the spaces developed on [25]. For this we followed the line of work of the thesis [16]. We see that, for scattered spaces the properties Rothberger, Menger and indestructibly Lindelöf are preserved for elementary submodels. Furthermore we continue to investigate these preservations for more general spaces. Finally we worked with spaces and elementary submodels. Este trabalho trata de dois tópicos distintos. Primeiro tratamos sobre a teoria das partições em espaços topológicos, desenvolvendo os tópicos explorados em [27]. Adaptamos a demonstração do primeiro teorema do artigo previamente citado. Também melhoramos a consistência de um resultado feito com , construindo um exemplo consistente com ¬. Com relação ao segundo tópico, desenvolvemos sobre os espaços definidos em [25]. Seguimos por um caminho semelhante ao feito na tese [16]. Vemos que, no caso de espaços dispersos, há preservação, com relação a submodelos elementares, para as propriedades de Rothberger, Menger e indestrutivelmente Lindelöf. Ademais continuamos a investigar tais reflexões para espaços mais gerais. Por fim, trabalhamos com espaços da forma () e submodelos elementares. https://doi.org/10.11606/T.45.2022.tde-12102022-112918info:eu-repo/semantics/openAccessengreponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USP2023-12-21T18:48:39Zoai:teses.usp.br:tde-12102022-112918Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212023-12-22T12:34:01.697379Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false |
dc.title.en.fl_str_mv |
Covering properties,reflections in elementary submodels and partitions on topological spaces |
dc.title.alternative.pt.fl_str_mv |
Propriedades de cobertura, reflexões em submodelos elementares e partições em espaços topológicos |
title |
Covering properties,reflections in elementary submodels and partitions on topological spaces |
spellingShingle |
Covering properties,reflections in elementary submodels and partitions on topological spaces Rodrigo Rey Carvalho |
title_short |
Covering properties,reflections in elementary submodels and partitions on topological spaces |
title_full |
Covering properties,reflections in elementary submodels and partitions on topological spaces |
title_fullStr |
Covering properties,reflections in elementary submodels and partitions on topological spaces |
title_full_unstemmed |
Covering properties,reflections in elementary submodels and partitions on topological spaces |
title_sort |
Covering properties,reflections in elementary submodels and partitions on topological spaces |
author |
Rodrigo Rey Carvalho |
author_facet |
Rodrigo Rey Carvalho |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Lucia Renato Junqueira |
dc.contributor.referee1.fl_str_mv |
Rodrigo Roque Dias |
dc.contributor.referee2.fl_str_mv |
Gabriel Zanetti Nunes Fernandes |
dc.contributor.referee3.fl_str_mv |
Renan Maneli Mezabarba |
dc.contributor.referee4.fl_str_mv |
Marcelo Dias Passos |
dc.contributor.author.fl_str_mv |
Rodrigo Rey Carvalho |
contributor_str_mv |
Lucia Renato Junqueira Rodrigo Roque Dias Gabriel Zanetti Nunes Fernandes Renan Maneli Mezabarba Marcelo Dias Passos |
description |
This work develops two distinct topics. We first work with partitions on topological spaces, developing some topics found on [27]. We fixed the proof of the first theorem from the previous paper. We also improved the consistency of a result obtained using by constructing an example consistent with ¬. In relation with the second topic we studied the spaces developed on [25]. For this we followed the line of work of the thesis [16]. We see that, for scattered spaces the properties Rothberger, Menger and indestructibly Lindelöf are preserved for elementary submodels. Furthermore we continue to investigate these preservations for more general spaces. Finally we worked with spaces and elementary submodels. |
publishDate |
2022 |
dc.date.issued.fl_str_mv |
2022-08-19 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://doi.org/10.11606/T.45.2022.tde-12102022-112918 |
url |
https://doi.org/10.11606/T.45.2022.tde-12102022-112918 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade de São Paulo |
dc.publisher.program.fl_str_mv |
Matemática |
dc.publisher.initials.fl_str_mv |
USP |
dc.publisher.country.fl_str_mv |
BR |
publisher.none.fl_str_mv |
Universidade de São Paulo |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da USP instname:Universidade de São Paulo (USP) instacron:USP |
instname_str |
Universidade de São Paulo (USP) |
instacron_str |
USP |
institution |
USP |
reponame_str |
Biblioteca Digital de Teses e Dissertações da USP |
collection |
Biblioteca Digital de Teses e Dissertações da USP |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP) |
repository.mail.fl_str_mv |
virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br |
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1794502689562820608 |