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manuscripta mathematica

, Volume 63, Issue 2, pp 215–231 | Cite as

Local semianalytic geometry

  • Robert O. Robson
Article

Abstract

This paper treats the theory of semianalytic function germs over real closed fields more general than ℝ. An ordered field is microbial if it has a non-zero element whose powers converge to zero. The fields we treat are direct limits of countable microbial subfields. We define local rings of analytic function germs algebraically and use the Weierstrass preparation theory to prove an Artin-Lang property. We end by relating seminash functions to abstract semialgebraic functions on the real spectrum of the local rings.

Keywords

Analytic Function Number Theory Algebraic Geometry Topological Group Local Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Robert O. Robson
    • 1
  1. 1.Department of MathematicsOregon State UniversityCorvallisUSA

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