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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| Veröffentlicht in: | Журнал математической физики, анализа, геометрии |
|---|---|
| Datum: | 2011 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/106684 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| id |
nasplib_isofts_kiev_ua-123456789-106684 |
|---|---|
| record_format |
dspace |
| spelling |
Giordano, P. 2016-10-02T19:31:37Z 2016-10-02T19:31:37Z 2011 Infinite Dimensional Spaces and Cartesian Closedness / P. Giordano // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 3. — С. 225-284. — Бібліогр.: 89 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106684 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Infinite Dimensional Spaces and Cartesian Closedness Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Infinite Dimensional Spaces and Cartesian Closedness |
| spellingShingle |
Infinite Dimensional Spaces and Cartesian Closedness Giordano, P. |
| title_short |
Infinite Dimensional Spaces and Cartesian Closedness |
| title_full |
Infinite Dimensional Spaces and Cartesian Closedness |
| title_fullStr |
Infinite Dimensional Spaces and Cartesian Closedness |
| title_full_unstemmed |
Infinite Dimensional Spaces and Cartesian Closedness |
| title_sort |
infinite dimensional spaces and cartesian closedness |
| author |
Giordano, P. |
| author_facet |
Giordano, P. |
| publishDate |
2011 |
| language |
English |
| container_title |
Журнал математической физики, анализа, геометрии |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
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.
|
| issn |
1812-9471 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/106684 |
| citation_txt |
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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2025-12-07T19:26:31Z |
| last_indexed |
2025-12-07T19:26:31Z |
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1850878817831223296 |