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Logical opens of exponential objects

Bruno, Oscar P. (1985) Logical opens of exponential objects. Cahiers de Topologie et Géométrie Différentielle Catégoriques, 26 (3). pp. 311-323. ISSN 1245-530X. https://resolver.caltech.edu/CaltechAUTHORS:20181107-080545986

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Abstract

Let X = C^∞(R^p)/J, Y = C^∞(R^n)/I be two representable objects in the Dubuc topos D (see Secsion 0) where J has line determined extensions (0.3). The main result in this paper (Theorem 1.11) says that the global section functor Γ establishes a bijection between Penon open sub-objects of Y^x and open subsets of Γ(Y^x) in the C^∞-CO topology. We show also that when I = {0}, we can assume J arbitrary (1.12). However, the restriction on J (of having line determined extensions) is seen to be unavoidable in general. We precede the article with a Section 0 where we recall all these notions and fix the notations.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://www.numdam.org/item/?id=CTGDC_1985__26_3_311_0PublisherArticle
ORCID:
AuthorORCID
Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 1985 Andrée C. Ehresmann et les auterus.
Issue or Number:3
Record Number:CaltechAUTHORS:20181107-080545986
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181107-080545986
Official Citation:Bruno, Oscar P. Logical opens of exponential objects. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume 26 (1985) no. 3, pp. 311-323. http://www.numdam.org/item/CTGDC_1985__26_3_311_0
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90687
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Nov 2018 17:52
Last Modified:03 Oct 2019 20:27

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