Objets compacts dans les topos

It is well known that compact topological spaces are those spaces K for which given any point x0 in any topological space X, and a neighborhood H of the fibre [formula omitted] then there exists a neighborhood U of x0 such that ∏−U⊂ H. If now [formula omitted] is an object in an arbitrary topos, in...

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Publicado: 1986
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v40_n2_p203_Dubuc
http://hdl.handle.net/20.500.12110/paper_14467887_v40_n2_p203_Dubuc
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spelling paper:paper_14467887_v40_n2_p203_Dubuc2023-06-08T16:16:08Z Objets compacts dans les topos It is well known that compact topological spaces are those spaces K for which given any point x0 in any topological space X, and a neighborhood H of the fibre [formula omitted] then there exists a neighborhood U of x0 such that ∏−U⊂ H. If now [formula omitted] is an object in an arbitrary topos, in the internal logic of the topos this property means that, for any A in Ω and B in ΩK, we have ∀∏(∏−1A ⊔ B) = A ⊔ ∀∏ B. We introduce this formula as a definition of compactness for objects in an arbitrary topos. Then we prove that in the gross topoi of algebraic, analytic, and differential geometry, this property characterizes exactly the complete varieties, the compact (analytic) spaces, and the compact manifolds, respectively. © 1986, Australian Mathematical Society. All rights reserved. 1986 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v40_n2_p203_Dubuc http://hdl.handle.net/20.500.12110/paper_14467887_v40_n2_p203_Dubuc
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description It is well known that compact topological spaces are those spaces K for which given any point x0 in any topological space X, and a neighborhood H of the fibre [formula omitted] then there exists a neighborhood U of x0 such that ∏−U⊂ H. If now [formula omitted] is an object in an arbitrary topos, in the internal logic of the topos this property means that, for any A in Ω and B in ΩK, we have ∀∏(∏−1A ⊔ B) = A ⊔ ∀∏ B. We introduce this formula as a definition of compactness for objects in an arbitrary topos. Then we prove that in the gross topoi of algebraic, analytic, and differential geometry, this property characterizes exactly the complete varieties, the compact (analytic) spaces, and the compact manifolds, respectively. © 1986, Australian Mathematical Society. All rights reserved.
title Objets compacts dans les topos
spellingShingle Objets compacts dans les topos
title_short Objets compacts dans les topos
title_full Objets compacts dans les topos
title_fullStr Objets compacts dans les topos
title_full_unstemmed Objets compacts dans les topos
title_sort objets compacts dans les topos
publishDate 1986
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v40_n2_p203_Dubuc
http://hdl.handle.net/20.500.12110/paper_14467887_v40_n2_p203_Dubuc
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