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Paper   IPM / M / 2294
School of Mathematics
  Title:   Pathological functions on Puiseux series ordered fields and others
  Author(s): 
1.  Moj. Moniri
2.  J. S. Eivazloo
  Status:   Published
  Journal: Lobachevskii J. Math.
  Vol.:  11
  Year:  2002
  Pages:   13-18
  Supported by:  IPM
  Abstract:
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.

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