We study three types of order convergence and related concepts of order continuous maps in partially ordered sets, partially ordered abelian groups, and partially ordered vector spaces, respectively. An order topology is introduced such that in the latter two settings under mild conditions order continuity is a topological property. We present a generalisation of the Ogasawara theorem on the structure of the set of order continuous operators.

中文翻译：

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从拓扑角度看顺序连续性

我们分别研究了偏序集合、偏序阿贝尔群和偏序向量空间中序连续映射的三种类型的阶收敛和相关概念。引入了有序拓扑，使得在温和条件下的后两种设置中，有序连续性是一种拓扑特性。我们在序连续算子集的结构上提出了 Ogasawara 定理的推广。