  Let $V$ be a valuation domain with quotient field $K$. Given a
pseudo-convergent sequence $E$ in $K$, we study two constructions associating
to $E$ a valuation domain of $K(X)$ lying over $V$, especially when $V$ has
rank one. The first one has been introduced by Ostrowski, the second one more
recently by Loper and Werner. We describe the main properties of these
valuation domains, and we give a notion of equivalence on the set of
pseudo-convergent sequences of $K$ characterizing when the associated valuation
domains are equal. Then, we analyze the topological properties of the
Zariski-Riemann spaces formed by these valuation domains.
