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

Elvio Accinelli and Enrique Covarrubias

No 2013-23, Working Papers from Banco de México

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.

JEL-codes: D5 D50 D51 (search for similar items in EconPapers)
Date: 2013-12
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Working Paper: An extension of the Sard-Smale Theorem to domains with an empty interior (2013)
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