We provide an exhaustive description of the class of locally convex spaces in which all Archimedean cones are closed. We introduce the notion of quasidense set and prove that the above class consists of all finite-dimensional and countable-dimensional spaces \( X \) whose topological dual \( X^{\prime} \) is quasidense in the algebraic dual \( X^{\#} \) of \( X \).

中文翻译：

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所有阿基米德锥体都闭合的局部凸空间

我们提供了所有阿基米德锥体都闭合的局部凸空间类的详尽描述。我们引入准邻集的概念，并证明上述类由所有有限维和可数维空间\( X \)组成 ，其拓扑对偶 \( X^{\prime} \)在代数对偶\( X^{\#} \)的\( X \)。