Necessary and sufficient conditions on a topology t on an arbitrary set X are presented, under which every not necessarily total preorder, which in addition satisfies a general continuity condition, namely weak continuity, admits a continuous order-preserving real-valued function. Some interesting properties associated with this notion are studied.

中文翻译：

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每种非总计弱连续预订的连续可表示性的拓扑

给出了在任意集合X上的拓扑t上的充要条件，在此条件下，每个未必一定是总的预序，而且还满足一般的连续性条件，即弱连续性，允许连续的保持阶数的实值函数。研究了与此概念相关的一些有趣的属性。