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Vector fields on R^R in well adapted models of synthetic differential geometry

Bruno, Oscar P. (1987) Vector fields on R^R in well adapted models of synthetic differential geometry. Journal of Pure and Applied Algebra, 45 (1). pp. 1-14. ISSN 0022-4049. https://resolver.caltech.edu/CaltechAUTHORS:20181101-152904132

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Abstract

Vector fields in infinite-dimensional manifolds play an important role in differential topology-geometry. In particular the case when the manifolds are C∞-map spaces. The well developed theory modeled in Banach spaces does not apply here. Instead a theory modeled in Frechet spaces is being considered. This is a theory which seems to be a much less straightforward generalization of the finite-dimensional case. The well adapted models of S.D.G. lead naturally to treat these spaces. We investigate here the case of the 'manifold' R^R, whose space of global sections is C^∞(ℝ). We prove that to integrate a vector field in R^R is equivalent to a certain differential problem in C^∞(ℝ). To do this, we previously characterize the maps R^R → R^R, R^R X R^R in the topos by means of the functions they induce in the respective spaces of global sections.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0022-4049(87)90080-6DOIArticle
ORCID:
AuthorORCID
Bruno, Oscar P.0000-0001-8369-3014
Alternate Title:Vector fields on RR in well adapted models of synthetic differential geometry
Additional Information:© 1987 Published by Elsevier. Under an Elsevier user license. Received 21 February 1985. Communicated by F.W. Lawvere.
Issue or Number:1
Record Number:CaltechAUTHORS:20181101-152904132
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181101-152904132
Official Citation:Oscar P. Bruno, Vector fields on RR in well adapted models of synthetic differential geometry, Journal of Pure and Applied Algebra, Volume 45, Issue 1, 1987, Pages 1-14, ISSN 0022-4049, https://doi.org/10.1016/0022-4049(87)90080-6. (http://www.sciencedirect.com/science/article/pii/0022404987900806)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90591
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:02 Nov 2018 18:48
Last Modified:03 Oct 2019 20:26

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