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Three problems concerning ideals of differentiable functions

Bruno, Oscar P. (1988) Three problems concerning ideals of differentiable functions. Journal of Pure and Applied Algebra, 53 (1-2). pp. 15-32. ISSN 0022-4049. https://resolver.caltech.edu/CaltechAUTHORS:20181101-152904050

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Abstract

In this paper, we study the validity of the following two statements in the internal logic of the toposes of Synthetic Differential Geometry: 1. (1) The integral of f is non-negative if f is non-negative; 2. (2) If f=0 in the set of non-negative reals, and f=0 in the set of non-negative reals, then f=0. We find statements (1) and (2) to be true in the toposes considered. We also prove that 3. (3) For n greater than two, the arrow tn from the line to itself is not a stable effective epic. This answers a question raised by Quê-Moerdijk-Reyes.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0022-4049(88)90009-6DOIArticle
ORCID:
AuthorORCID
Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 1988 Published by Elsevier. Under an Elsevier user license. Communicated by F. W. Lawvere. Received 29 December 1986. Research partially supported by the “Groupe Interuniversitaire en Etudes Categoriques”. We thank Gonzalo Reyes and van Quê for suggesting the problems and for their encouragement.
Funders:
Funding AgencyGrant Number
Groupe Interuniversitaire en Etudes CategoriquesUNSPECIFIED
Issue or Number:1-2
Record Number:CaltechAUTHORS:20181101-152904050
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181101-152904050
Official Citation:Oscar P. Bruno, Three problems concerning ideals of differentiable functions, Journal of Pure and Applied Algebra, Volume 53, Issues 1–2, 1988, Pages 15-32, ISSN 0022-4049, https://doi.org/10.1016/0022-4049(88)90009-6. (http://www.sciencedirect.com/science/article/pii/0022404988900096)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90590
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:01 Nov 2018 23:12
Last Modified:03 Oct 2019 20:26

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