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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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 |
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R-134 |
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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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1807321241159204864 |