On the algebraic representation of semicontinuity
Autor(a) principal: | |
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Data de Publicação: | 2007 |
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/10316/4600 https://doi.org/10.1016/j.jpaa.2006.09.004 |
Resumo: | The concepts of upper and lower semicontinuity in pointfree topology were introduced and first studied by Li and Wang [Y.-M. Li, G.-J. Wang, Localic Katetov-Tong insertion theorem and localic Tietze extension theorem, Comment. Math. Univ. Carolin. 38 (1997) 801-814]. However Li and Wang's treatment does not faithfully reflect the original classical notion. In this note, we present algebraic descriptions of upper and lower semicontinuous real functions, in terms of frame homomorphisms, that suggest the right alternative to the definitions of Li and Wang. This fixes the discrepancy between the classical and the pointfree notions and turns out to be the appropriate notion that makes the Katetov-Tong theorem provable in the pointfree context without any restrictions. |
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On the algebraic representation of semicontinuityThe concepts of upper and lower semicontinuity in pointfree topology were introduced and first studied by Li and Wang [Y.-M. Li, G.-J. Wang, Localic Katetov-Tong insertion theorem and localic Tietze extension theorem, Comment. Math. Univ. Carolin. 38 (1997) 801-814]. However Li and Wang's treatment does not faithfully reflect the original classical notion. In this note, we present algebraic descriptions of upper and lower semicontinuous real functions, in terms of frame homomorphisms, that suggest the right alternative to the definitions of Li and Wang. This fixes the discrepancy between the classical and the pointfree notions and turns out to be the appropriate notion that makes the Katetov-Tong theorem provable in the pointfree context without any restrictions.http://www.sciencedirect.com/science/article/B6V0K-4M93BV4-1/1/83eca38a0e6ca12609ed146ae7a6ed062007info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleaplication/PDFhttp://hdl.handle.net/10316/4600http://hdl.handle.net/10316/4600https://doi.org/10.1016/j.jpaa.2006.09.004engJournal of Pure and Applied Algebra. 210:2 (2007) 299-306Gutiérrez García, J.Picado, Jorgeinfo: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:RCAAP2021-09-13T11:02:43Zoai:estudogeral.uc.pt:10316/4600Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:41.297149Repositório 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 |
On the algebraic representation of semicontinuity |
title |
On the algebraic representation of semicontinuity |
spellingShingle |
On the algebraic representation of semicontinuity Gutiérrez García, J. |
title_short |
On the algebraic representation of semicontinuity |
title_full |
On the algebraic representation of semicontinuity |
title_fullStr |
On the algebraic representation of semicontinuity |
title_full_unstemmed |
On the algebraic representation of semicontinuity |
title_sort |
On the algebraic representation of semicontinuity |
author |
Gutiérrez García, J. |
author_facet |
Gutiérrez García, J. Picado, Jorge |
author_role |
author |
author2 |
Picado, Jorge |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Gutiérrez García, J. Picado, Jorge |
description |
The concepts of upper and lower semicontinuity in pointfree topology were introduced and first studied by Li and Wang [Y.-M. Li, G.-J. Wang, Localic Katetov-Tong insertion theorem and localic Tietze extension theorem, Comment. Math. Univ. Carolin. 38 (1997) 801-814]. However Li and Wang's treatment does not faithfully reflect the original classical notion. In this note, we present algebraic descriptions of upper and lower semicontinuous real functions, in terms of frame homomorphisms, that suggest the right alternative to the definitions of Li and Wang. This fixes the discrepancy between the classical and the pointfree notions and turns out to be the appropriate notion that makes the Katetov-Tong theorem provable in the pointfree context without any restrictions. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/4600 http://hdl.handle.net/10316/4600 https://doi.org/10.1016/j.jpaa.2006.09.004 |
url |
http://hdl.handle.net/10316/4600 https://doi.org/10.1016/j.jpaa.2006.09.004 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Pure and Applied Algebra. 210:2 (2007) 299-306 |
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info:eu-repo/semantics/openAccess |
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openAccess |
dc.format.none.fl_str_mv |
aplication/PDF |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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