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Zh. Mat. Fiz. Anal. Geom., 2011, Volume 7, Number 3, Pages 225–284 (Mi jmag514)  

This article is cited in 2 scientific papers (total in 2 papers)

Infinite dimensional spaces and cartesian closedness

Paolo Giordano

Department of Mathematics, University of Vienna, Nordbergstr 15, 1090 Wien, Austria

Abstract: 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.

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Document Type: Article
MSC: 58Bxx, 53Z05, 58B25
Received: 19.03.2010
Language: English

Citation: Paolo Giordano, “Infinite dimensional spaces and cartesian closedness”, Zh. Mat. Fiz. Anal. Geom., 7:3 (2011), 225–284

Citation in format AMSBIB
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\by Paolo Giordano
\paper Infinite dimensional spaces and cartesian closedness
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2011
\vol 7
\issue 3
\pages 225--284
\mathnet{http://mi.mathnet.ru/jmag514}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2918489}
\zmath{https://zbmath.org/?q=an:1237.58010}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000301173200003}


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  • http://mi.mathnet.ru/eng/jmag/v7/i3/p225

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Giordano P., Wu E., “Categorical Frameworks For Generalized Functions”, Arabian J. Math., 4:4, SI (2015), 301–328  crossref  mathscinet  zmath  isi
    2. Giordano P., Wu E., “Calculus in the Ring of Fermat Reals, Part i: Integral Calculus”, Adv. Math., 289 (2016), 888–927  crossref  mathscinet  zmath  isi
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