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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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.

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

First available in Project Euclid: 26 July 2016

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Zentralblatt MATH identifier

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

Real places spaces of real places


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.

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