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Abstract:

Let [formula-omitted] be any ideal. Since a function of the variables [formula-omitted] is a function of the variables [formula-omitted] which does not depend on [formula-omitted], we have [formula-omitted]. Of course, J is not an ideal of C∞ (IRn+P), but it generates an ideal that we call [formula-omitted]. Consider the following statement (1) on J: “Given any [formula-omitted] if and only if for every fixed [formula-omitted]. In this paper we show that statement (1) holds for a large class of finitely generated ideals although not for all of them. We say that ideals satisfying statement (1) have line determined extensions. We characterize these ideals to be closed ideals ([formula-omitted](in the sense of Whitney) such that for all [formula-omitted], the ideal [formula-omitted] is also closed. Finally, some non-trivial examples are developed. © 1986, Australian Mathematical Society. All rights reserved.

Registro:

Documento: Artículo
Título:On a property of ideals of differentiable functions
Autor:Bruno, O.P.
Filiación:Cuidad Universitaria, Depto de Mathematics, Pab. no. 1, 1428 - BUENOS AIRES, Argentina
Año:1986
Volumen:33
Número:2
Página de inicio:293
Página de fin:305
DOI: http://dx.doi.org/10.1017/S0004972700003166
Título revista:Bulletin of the Australian Mathematical Society
Título revista abreviado:Bull. Aust. Math. Soc.
ISSN:00049727
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00049727_v33_n2_p293_Bruno

Referencias:

  • Dubuc, E., C∞-Schemes (1981) Amer. J. Math., 103, pp. 683-690
  • Malgrange, B., (1966) Ideals of Differentiable Functions, , (OUP)
  • Reyes, G.E., Van Quê, N., Smooth functors and synthetic calculus (1982) The L.E.J. Brouwer Centenary Symposium, pp. 377-395. , Troelstra A. S., Van Dalen D., (eds.), (North Holland
  • Weil, A., Theorie des points proches sur les variétés différetiables (1953) Géométrie différentielle, pp. 111-117. , (Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourt, 1953., Centre National de la Recherche Scientifique, Paris
  • Whitney, H., On ideals of differentiable functions (1948) Amer. J. Math., 70, pp. 635-658

Citas:

---------- APA ----------
(1986) . On a property of ideals of differentiable functions. Bulletin of the Australian Mathematical Society, 33(2), 293-305.
http://dx.doi.org/10.1017/S0004972700003166
---------- CHICAGO ----------
Bruno, O.P. "On a property of ideals of differentiable functions" . Bulletin of the Australian Mathematical Society 33, no. 2 (1986) : 293-305.
http://dx.doi.org/10.1017/S0004972700003166
---------- MLA ----------
Bruno, O.P. "On a property of ideals of differentiable functions" . Bulletin of the Australian Mathematical Society, vol. 33, no. 2, 1986, pp. 293-305.
http://dx.doi.org/10.1017/S0004972700003166
---------- VANCOUVER ----------
Bruno, O.P. On a property of ideals of differentiable functions. Bull. Aust. Math. Soc. 1986;33(2):293-305.
http://dx.doi.org/10.1017/S0004972700003166