Rocky Mountain Journal of Mathematics

The structure of spaces of $\mathbb{R}$-places of rational function fields over real closed fields

Katarzyna Kuhlmann

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Abstract

For arbitrary real closed fields $R$, we study the structure of the space $M(R(y))$ of $\mathbb{R}$-places of the rational function field in one variable over $R$ and determine its dimension to be 1. We determine small subbases for its topology and discuss a suitable metric in the metrizable case. In the case of non-archimedean $R$, we exhibit the rich variety of homeomorphisms of subspaces that can be found in such spaces.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 2 (2016), 533-557.

Dates
First available in Project Euclid: 26 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1469537476

Digital Object Identifier
doi:10.1216/RMJ-2016-46-2-533

Mathematical Reviews number (MathSciNet)
MR3529082

Zentralblatt MATH identifier
1380.12009

Subjects
Primary: 13J30: Real algebra [See also 12D15, 14Pxx]
Secondary: 12J15: Ordered fields 12J25: Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10] 54E45: Compact (locally compact) metric spaces

Keywords
Real places spaces of real places

Citation

Kuhlmann, Katarzyna. The structure of spaces of $\mathbb{R}$-places of rational function fields over real closed fields. Rocky Mountain J. Math. 46 (2016), no. 2, 533--557. doi:10.1216/RMJ-2016-46-2-533. https://projecteuclid.org/euclid.rmjm/1469537476


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References

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