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Nonexpansive Mappings and Zermelo’s Theorem

In: Fixed Point Theory in Distance Spaces

Author

Listed:
  • William Kirk

    (University of Iowa, Department of Mathematics)

  • Naseer Shahzad

    (King Abdulaziz University, Department of Mathematics)

Abstract

An extension of a theorem attributed variously to Zermelo, Bourbaki, and Kneser provides the basis for Mańka’s proof that Caristi’s theorem holds in ZF. In the sequel we shall simply refer to this theorem as Zermelo’s theorem Zermelo’s theorem . This theorem should NOT be confused with the celebrated well-ordering theorem also due to Zermelo, which is equivalent to the Axiom of Choice. See A.3 and A.9 of [107] for a brief discussion of constructive aspects of mathematics.

Suggested Citation

  • William Kirk & Naseer Shahzad, 2014. "Nonexpansive Mappings and Zermelo’s Theorem," Springer Books, in: Fixed Point Theory in Distance Spaces, edition 127, chapter 0, pages 19-22, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-10927-5_3
    DOI: 10.1007/978-3-319-10927-5_3
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