Nonexpansive Mappings and Zermelo’s Theorem

William Kirk and Naseer Shahzad
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William Kirk: University of Iowa, Department of Mathematics
Naseer Shahzad: King Abdulaziz University, Department of Mathematics

Chapter Chapter 3 in Fixed Point Theory in Distance Spaces, 2014, pp 19-22 from Springer

Abstract: 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.

Keywords: Nonexpansive Mappings; Zermelo's Theorem; Bourbaki; Convexity Structures; Hyperconvex (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-10927-5_3

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