论文标题
与伪构序序列相关的评估域空间的衡量性
Metrizability of spaces of valuation domains associated to pseudo-convergent sequences
论文作者
论文摘要
让$ v $是一个与商字段$ k $的等级第一的估值域。我们从拓扑的角度研究了由$ k $引起的理性功能领域$ k（x）$的$ v $的扩展名，从拓扑角度来看，与Zariski或可构造拓扑结构赋予了这套集合。特别是，我们考虑了由规定的宽度或规定的伪限制的序列引起的两个子空间。我们为Zariski空间提供了一些必要的条件，可以在价值组和$ v $的残留场方面进行Metrizable（在可构造拓扑结构下）。
Let $V$ be a valuation domain of rank one with quotient field $K$. We study the set of extensions of $V$ to the field of rational functions $K(X)$ induced by pseudo-convergent sequences of $K$ from a topological point of view, endowing this set either with the Zariski or with the constructible topology. In particular, we consider the two subspaces induced by sequences with a prescribed breadth or with a prescribed pseudo-limit. We give some necessary conditions for the Zariski space to be metrizable (under the constructible topology) in terms of the value group and the residue field of $V$.
