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.
Citation
Katarzyna Kuhlmann. "The structure of spaces of $\mathbb{R}$-places of rational function fields over real closed fields." Rocky Mountain J. Math. 46 (2) 533 - 557, 2016. https://doi.org/10.1216/RMJ-2016-46-2-533
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