This article is cited in 2 scientific papers (total in 2 papers)
Infinite dimensional spaces and cartesian closedness
Department of Mathematics, University of Vienna, Nordbergstr 15, 1090 Wien, Austria
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.
Key words and phrases:
infinite dimensional spaces of smooth mappings, diffelogy, synthetic differential geometry, cartesian closedness.
PDF file (496 kB)
MSC: 58Bxx, 53Z05, 58B25
Paolo Giordano, “Infinite dimensional spaces and cartesian closedness”, Zh. Mat. Fiz. Anal. Geom., 7:3 (2011), 225–284
Citation in format AMSBIB
\by Paolo Giordano
\paper Infinite dimensional spaces and cartesian closedness
\jour Zh. Mat. Fiz. Anal. Geom.
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