Artículo
Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | Objets compacts dans les topos |
| Autor: | Dubuc, E.J.; Penon, J. |
| Filiación: | Departamento de Matematicas, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina U.E.R. de Mathématiques, Université de Paris VII, Tours 4555, 2 Place Jussieu, 75005 Paris, France |
| Año: | 1986 |
| Volumen: | 40 |
| Número: | 2 |
| Página de inicio: | 203 |
| Página de fin: | 217 |
| DOI: | http://dx.doi.org/10.1017/S144678870002718X |
| Título revista: | Journal of the Australian Mathematical Society |
| Título revista abreviado: | J. Aust. Math. Soc. |
| ISSN: | 14467887 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v40_n2_p203_Dubuc |
Referencias:
- Dubuc, E.J., Sur les modeles de la géométrie différentielle synthétique (1979) Cahiers Topologie Geom. Différentielle, XX-3
- Dubuc, E.J., Open covers and infinitary operations in C∞-rings (1981) XXII-3
- Dubuc, E.J., C∞-schemes (1981) Amer. J. Math., 103, pp. 683-690
- Hakim, M., Topos annales et schemas relatif (1972) Ergeb. Math. Grenzgeb., 64. , Springer-Verlag, Berlin, Heidelberg, New York
- Kock, A., Universal projective geometry; via topos theory (1976) J. Pure Appl. Algebra, 9, pp. 1-24
- Kock, A., (1981) Synthetic differential geometry, , Cambridge University Press, Cambridge, England
- Malgrange, B., (1968) Analytic spaces, , Monographic N° 17 de l'Enseignement Mathematique, Genéve
- Penon, J., Topologie et intuitionnisme (1981) Journées Faisceaux et Logique, , Mai, (Universite Paris-Nord, pré-publications Mathematique (1982))
- Penon, J., , 7. , Manuscrits non-publiés, a paraitre dans la these de doctorat, Paris; Spivak, M., A comprehensive introduction to differential geometry (1970) Publish or Perish, 1. , Brandeis University
Citas:
---------- APA ----------
Dubuc, E.J. & Penon, J. (1986) . Objets compacts dans les topos. Journal of the Australian Mathematical Society, 40(2), 203-217.http://dx.doi.org/10.1017/S144678870002718X
---------- CHICAGO ----------
Dubuc, E.J., Penon, J. "Objets compacts dans les topos" . Journal of the Australian Mathematical Society 40, no. 2 (1986) : 203-217.http://dx.doi.org/10.1017/S144678870002718X
---------- MLA ----------
Dubuc, E.J., Penon, J. "Objets compacts dans les topos" . Journal of the Australian Mathematical Society, vol. 40, no. 2, 1986, pp. 203-217.http://dx.doi.org/10.1017/S144678870002718X
---------- VANCOUVER ----------
Dubuc, E.J., Penon, J. Objets compacts dans les topos. J. Aust. Math. Soc. 1986;40(2):203-217.http://dx.doi.org/10.1017/S144678870002718X
