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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Autores principales: Dubuc, E.J., Penon, J.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_14467887_v40_n2_p203_Dubuc
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spelling todo:paper_14467887_v40_n2_p203_Dubuc2023-10-03T16:16:29Z Objets compacts dans les topos Dubuc, E.J. Penon, J. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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.
format JOUR
author Dubuc, E.J.
Penon, J.
spellingShingle Dubuc, E.J.
Penon, J.
Objets compacts dans les topos
author_facet Dubuc, E.J.
Penon, J.
author_sort Dubuc, E.J.
title 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
url http://hdl.handle.net/20.500.12110/paper_14467887_v40_n2_p203_Dubuc
work_keys_str_mv AT dubucej objetscompactsdanslestopos
AT penonj objetscompactsdanslestopos
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