More on Subfitness and Fitness
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/43793 https://doi.org/10.1007/s10485-014-9366-7 |
Resumo: | The concepts of fitness and subfitness (as defined in Isbell, Trans. Amer. Math. Soc. 327, 353–371, 1991) are useful separation properties in point-free topology. The categorical behaviour of subfitness is bad and fitness is the closest modification that behaves well. The separation power of the two, however, differs very substantially and subfitness is transparent and turns out to be useful in its own right. Sort of supplementing the article (Simmons, Appl. Categ. Struct. 14, 1–34, 2006) we present several facts on these concepts and their relation. First the “supportive” role subfitness plays when added to other properties is emphasized. In particular we prove that the numerous Dowker-Strauss type Hausdorff axioms become one for subfit frames. The aspects of fitness as a hereditary subfitness are analyzed, and a simple proof of coreflectivity of fitness is presented. Further, another property, prefitness, is shown to also produce fitness by heredity, in this case in a way usable for classical spaces, which results in a transparent characteristics of fit spaces. Finally, the properties are proved to be independent. |
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More on Subfitness and FitnessThe concepts of fitness and subfitness (as defined in Isbell, Trans. Amer. Math. Soc. 327, 353–371, 1991) are useful separation properties in point-free topology. The categorical behaviour of subfitness is bad and fitness is the closest modification that behaves well. The separation power of the two, however, differs very substantially and subfitness is transparent and turns out to be useful in its own right. Sort of supplementing the article (Simmons, Appl. Categ. Struct. 14, 1–34, 2006) we present several facts on these concepts and their relation. First the “supportive” role subfitness plays when added to other properties is emphasized. In particular we prove that the numerous Dowker-Strauss type Hausdorff axioms become one for subfit frames. The aspects of fitness as a hereditary subfitness are analyzed, and a simple proof of coreflectivity of fitness is presented. Further, another property, prefitness, is shown to also produce fitness by heredity, in this case in a way usable for classical spaces, which results in a transparent characteristics of fit spaces. Finally, the properties are proved to be independent.Springer2014info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43793http://hdl.handle.net/10316/43793https://doi.org/10.1007/s10485-014-9366-7https://doi.org/10.1007/s10485-014-9366-7enghttps://link.springer.com/article/10.1007/s10485-014-9366-7Picado, JorgePultr, Alešinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2021-06-29T10:02:53Zoai:estudogeral.uc.pt:10316/43793Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:27.864077Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
More on Subfitness and Fitness |
title |
More on Subfitness and Fitness |
spellingShingle |
More on Subfitness and Fitness Picado, Jorge |
title_short |
More on Subfitness and Fitness |
title_full |
More on Subfitness and Fitness |
title_fullStr |
More on Subfitness and Fitness |
title_full_unstemmed |
More on Subfitness and Fitness |
title_sort |
More on Subfitness and Fitness |
author |
Picado, Jorge |
author_facet |
Picado, Jorge Pultr, Aleš |
author_role |
author |
author2 |
Pultr, Aleš |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Picado, Jorge Pultr, Aleš |
description |
The concepts of fitness and subfitness (as defined in Isbell, Trans. Amer. Math. Soc. 327, 353–371, 1991) are useful separation properties in point-free topology. The categorical behaviour of subfitness is bad and fitness is the closest modification that behaves well. The separation power of the two, however, differs very substantially and subfitness is transparent and turns out to be useful in its own right. Sort of supplementing the article (Simmons, Appl. Categ. Struct. 14, 1–34, 2006) we present several facts on these concepts and their relation. First the “supportive” role subfitness plays when added to other properties is emphasized. In particular we prove that the numerous Dowker-Strauss type Hausdorff axioms become one for subfit frames. The aspects of fitness as a hereditary subfitness are analyzed, and a simple proof of coreflectivity of fitness is presented. Further, another property, prefitness, is shown to also produce fitness by heredity, in this case in a way usable for classical spaces, which results in a transparent characteristics of fit spaces. Finally, the properties are proved to be independent. |
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2014 |
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2014 |
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info:eu-repo/semantics/article |
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article |
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dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/43793 http://hdl.handle.net/10316/43793 https://doi.org/10.1007/s10485-014-9366-7 https://doi.org/10.1007/s10485-014-9366-7 |
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http://hdl.handle.net/10316/43793 https://doi.org/10.1007/s10485-014-9366-7 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
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https://link.springer.com/article/10.1007/s10485-014-9366-7 |
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info:eu-repo/semantics/openAccess |
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openAccess |
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Springer |
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Springer |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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