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. doi:10.1016/0022-4049(88)90009-6. 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 | ||||||
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| 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. | ||||||
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| Issue or Number: | 1-2 | ||||||
| DOI: | 10.1016/0022-4049(88)90009-6 | ||||||
| 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: | 16 Nov 2021 03:33 |
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