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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     author = {M. Moniri and J. S. Eivazloo},
     title = {Pathological functions on {Puiseux} series ordered fields and others},
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     url = {http://geodesic.mathdoc.fr/item/LJM_2002_11_a2/}
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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/