论文标题
二元关系的特性有多罕见？
How rare are the properties of binary relations?
论文作者
论文摘要
Knoblauch（2014）和Knoblauch（2015）与使用对称差异度量（Cantor）拓扑和Hausdorff度量拓扑相比，研究了具有理想特征的二元关系收集的相对大小。我们考虑Ellentuck和Donut Topologies，以进一步调查。我们报告了Cantor，Ellentuck和Donut Tupologies中有用的二进制关系大小之间的差异。事实证明，甜甜圈拓扑结构与其他两个相比，具有更一般特性的二进制关系。我们进一步证明，在诱发的康托克和埃伦塔克拓扑结构中，后者捕获了所有准词的集合中部分订单的相对规模。最后，我们证明，埃伦塔克（因此在坎托）拓扑中的道德二进制关系类别很小，但在甜甜圈拓扑中并不小。从本质上讲，与Cantor拓扑相比，Ellentuck拓扑票价更好，以捕获二进制关系的相对规模。
Knoblauch (2014) and Knoblauch (2015) investigate the relative size of the collection of binary relations with desirable features as compared to the set of all binary relations using symmetric difference metric (Cantor) topology and Hausdorff metric topology. We consider Ellentuck and doughnut topologies to further this line of investigation. We report the differences among the size of the useful binary relations in Cantor, Ellentuck and doughnut topologies. It turns out that the doughnut topology admits binary relations with more general properties in contrast to the other two. We further prove that among the induced Cantor and Ellentuck topologies, the latter captures the relative size of partial orders among the collection of all quasi-orders. Finally we show that the class of ethical binary relations is small in Ellentuck (and therefore in Cantor) topology but is not small in doughnut topology. In essence, the Ellentuck topology fares better compared to Cantor topology in capturing the relative size of collections of binary relations.
