An ordered topological vector space has the countable dominated extension property if any linear operator ranging in this space, defined on a subspace of a separable metrizable topological vector space, and dominated there by a continuous sublinear operator admits extension to the entire space with preservation of linearity and domination. Our main result is that the strong $$\sigma$$ -interpolation property is a necessary and sufficient condition for a sequentially complete topological vector space ordered by a closed normal reproducing cone to have the countable dominated extension property. Moreover, this fact can be proved in Zermelo–Fraenkel set theory with the axiom of countable choice.

中文翻译：

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关于线性算子的支配扩张

有序拓扑向量空间具有可数支配可拓性质，如果任何线性算子在该空间范围内，定义在可分离的可度量拓扑向量空间的子空间上，并由连续亚线性算子支配，允许扩展到整个空间并保持线性和统治。我们的主要结果是，强 $$\sigma$$ -interpolation 属性是由封闭法线再生锥排序的顺序完整拓扑向量空间具有可数主导扩展属性的必要和充分条件。此外，这一事实可以在带有可数选择公理的 Zermelo-Fraenkel 集合论中得到证明。