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An Extension of the Sard-Smale Theorem to Domains with an Empty Interior

Author

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  • Accinelli Elvio
  • Covarrubias Enrique
Abstract
A stumbling block in the modelling of competitive markets with commodity and price spaces of infinite dimensions, arises from having positive cones with an empty interior. This issue precludes the use of tools of differential analysis, ranging from the definition of a derivative, to the use of more sophisticated results needed to understand determinacy of equilibria and, more generally, the structure of the equilibrium set. To overcome these issues, this paper extends the Preimage Theorem and the Sard-Smale Theorem to maps between spaces that may have an empty interior.

Suggested Citation

  • Accinelli Elvio & Covarrubias Enrique, 2013. "An Extension of the Sard-Smale Theorem to Domains with an Empty Interior," Working Papers 2013-23, Banco de México.
    • Handle: RePEc:bdm:wpaper:2013-23
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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