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Differentiable Order Homomorphisms

  • Douglas S. Bridges
  • Ghanshyam B. Mehta
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 422)

Abstract

This chapter deals with the representation of a total preorder on a differentiable manifold by a differentiable order isomorphism. Section 1 contains basic definitions, and the fundamental theorem of Frobenius, from manifold theory. Using that theorem, we establish in Section 2 the existence of local differentiable order isomorphisms. Finally, in Section 3, we prove the existence of differentiable order isomorphisms.

Keywords

Open Subset Tangent Space Implicit Function Theorem Integral Manifold Differentiable Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Douglas S. Bridges
    • 1
  • Ghanshyam B. Mehta
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of WaikatoHamiltonNew Zealand
  2. 2.Department of EconomicsUniversity of QueenslandBrisbaneAustralia

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