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ЖУРНАЛЫ // Lobachevskii Journal of Mathematics // Архив

Lobachevskii J. Math., 2002, том 11, страницы 13–18 (Mi ljm115)

Pathological functions on Puiseux series ordered fields and others

M. Moniria, J. S. Eivazloo

a Institute for Studies in Theoretical Physics and Mathematics

Аннотация: 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.

Ключевые слова: ordered fields, gaps, Scott completeness, monotone completeness, cofinality, open maps, Puiseux series.

Представлено: М. М. Арсланов
Поступило: 14.05.2002

Язык публикации: английский



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