Infinite Dimensional Spaces and Cartesian Closedness
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Infinite Dimensional Spaces and Cartesian Closedness
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| Creator |
Giordano, P.
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| 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.
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| Date |
2016-10-02T19:31:37Z
2016-10-02T19:31:37Z 2011 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/106684 |
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| Language |
en
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| Relation |
Журнал математической физики, анализа, геометрии
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| Publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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