Infinite Dimensional Spaces and Cartesian Closedness
Infinite dimensional spaces frequently appear in physics; there are several approaches to obtain a good categorical framework for this type of space, and cartesian closedness of some category, embedding smooth manifolds, is one of the most requested condition. In the first part of the paper, we star...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2011 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106684 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Infinite Dimensional Spaces and Cartesian Closedness / P. Giordano // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 3. — С. 225-284. — Бібліогр.: 89 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Infinite dimensional spaces frequently appear in physics; there are several approaches to obtain a good categorical framework for this type of space, and cartesian closedness of some category, embedding smooth manifolds, is one of the most requested condition. In the first part of the paper, we start from the failures presented by the classical Banach manifolds approach and we will review the most studied approaches focusing on cartesian closedness: the convenient setting, diffeology and synthetic differential geometry. In the second part of the paper, we present a general settings to obtain cartesian closedness. Using this approach, we can also easily obtain the possibility to extend manifolds using nilpotent infinitesimal points, without any need to have a background in formal logic.
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| ISSN: | 1812-9471 |