Geodesic
Pathological functions on Puiseux series ordered fields and others
Lobachevskii journal of mathematics, Tome 11 (2002), pp. 13-18.

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We show that over closed bounded intervals in certain Archimedean ordered fields as well as in all non-Archimedean ones of countable cofinality, there are uniformly continuous 1-1 functions not mapping interior to interior. For the latter kind of fields, there are also uniformly continuous 1-1 functions mapping all interior points to interior points of the image which are, nevertheless, not open. In particular the ordered Laurent and Puiseux series fields with coefficients in any ordered field accommodate both kinds of such strange functions.
Keywords: ordered fields, gaps, Scott completeness, monotone completeness, cofinality, open maps
Mots-clés : Puiseux series. 
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M. Moniri; J. S. Eivazloo. Pathological functions on Puiseux series ordered fields and others. Lobachevskii journal of mathematics, Tome 11 (2002), pp. 13-18. http://geodesic.mathdoc.fr/item/LJM_2002_11_a2/

[1] H. J. Keisler, “Monotone Complete Fields”, Victoria Symposium on Nonstanard Analysis, Lecture Notes in Mathematics, 369, eds. A. Hurd and P. Loeb, Springer-Verlag, Berlin, 1974, 113–115 | MR

[2] M. Moniri and J. S. Eivazloo, “Using Nets in Dedekind, Monotone, or Scott Incomplete Ordered Fields and Definability Issues”, Proceedings of the Ninth Prague Topological Symposium, ed. P. Simon, Toronto, 2002, 195–203 ; Topology Atlas (available electronically at ) http://at.yorku.ca | MR | Zbl

[3] M. Moniri and J. S. Eivazloo, Abstract of a talk at Algebra Conference, Venezia, 2002 | MR

[4] P. Ribenboim, “Fields: Algebraically Closed and Others”, Manuscripta Math., 75 (1992), 115–150 | DOI | MR | Zbl

[5] J. H. Schmerl, “Models of Peano Arithmetic and a Question of Sikorski on Ordered Fields”, Israel J. Math., 50 (1985), 145–159 | DOI | MR | Zbl