Spaces of $\mathbb R$ - places of rational function fields

Details Spaces of $\mathbb R$ - places of rational function fields Spaces of $\mathbb R$ - places of rational function fields

2008-03-05

arxiv.org/abs/0803.0676v1

Mathematics

Commutative Algebra

16 pages

Scientific paper

In the paper an answer to a problem "When different orders of R(X) (where R
is a real closed field) lead to the same real place ?" is given. We use this
result to show that the space of $\mathbb R$-places of the field
$\textbf{R}(Y)$ (where \textbf{R} is any real closure of $\mathbb R(X)$) is not
metrizable space. Thus the space $M(\mathbb R(X,Y))$ is not metrizable, too.

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