论文标题
半连续的Richter-Peleg多功能表示的表征
Characterization of the existence of semicontinuous Richter-Peleg multi-utility representations
论文作者
论文摘要
对称拓扑空间中偏好关系的效用表示具有充分表征这些关系的优势。但是，在偏好关系表示的情况下，这并不是这样，这些关系主要不完整并且使用了不对称的拓扑。为了避免这种不幸的情况，由于缺乏对称性，Minguzzi [24]首先引入和研究了半连续的Richter-Peleg多功能表示的概念。通常，对半连续函数的研究表明，拓扑和顺序是同一数学对象的两个方面，因此应共同研究。该数学对象是比特学预分排空间的概念，它也构成了数学工具，以建模和分析不对称性和二元性的概念。在本文中，我们表征了比特波学空间中半连续的Richter-Peleg多功能表示的存在。基于此特征，我们证明了预订的$ \ precsim $具有所有Scott的集合，并且仅当$ \ precsim $在Erne的感觉上是前提[17]时，只有$ \ precsim $才能前进，并且仅当$ \ precsim $才能成为Richter-Peleg多UTI-UTILISE表示形式。
Utility representations of preference relations in symmetric topological spaces have the advantage of fully characterising these relations. But, this is not true in the case of representations of preference relations that are mostly incomplete and use asymmetric topologies. In order to avoid this unfortunate circumstance, due to lack of symmetry, the notion of semicontinuous Richter-Peleg multi-utility representation was first introduced and studied by Minguzzi [24]. Generally, the study of semicontinuous functions reveals that topology and order are two aspects of the same mathematical object and, therefore, should be studied jointly. This mathematical object is the notion of bitopological preordered space, which also constitutes the mathematical tool to model and analyse the notions of asymmetry and duality. In this paper, we characterize the existence of semicontinuous Richter-Peleg multi-utility representations in bitopological spaces. Based on this characterization, we prove that a preorder $\precsim$ has the set of all Scott and $ω$-continuous functions as Richter-Peleg multi-utility representation if and only if $\precsim$ is precontinuous in the sense of Erne [17].
