A Set of Independent Postulates for Cyclic Order.
A Set of Independent Postulates for Cyclic Order.
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一组循环顺序的独立假设。
DOI：
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发表时间：
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影响因子：
11.1
通讯作者：
E. V. Huntington
中科院分区：
文献类型：
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作者：
E. V. Huntington
有四种类型的序在几何和数学的其他分支中很重要：（la）沿着具有明确意义的线性序（序列顺序理论）;（lb）无意义区分的线性顺序（介数理论）;（2a）围绕圆有明确意义的圆序（理论的循环秩序）和（2b）循环秩序没有区别的意义（理论的分离点对）。本注记涉及类型（2a）：循环序。让我们考虑元素A，B，C，.的类K。. .和三元关系R（ABC）。如果满足以下假设，则可以说类K由关系R循环排序：
There are four types of order which are important in geometry and other branches of mathematics: (la) linear order with a definite sense along the line (theory of serial order); (lb) linear order without distinction of sense (theory of betweenness); (2a) circular order with a definite sense around the circle (theory of cyclic order); and (2b) circular order without distinction of sense (theory of separation of pairs of points). The present note is concerned with type (2a): cyclic order. Let us consider a class K of elements A, B, C, . . . , and a triadic relation R(ABC). The class K may be said to be cyclically ordered by the relation R if the following postulates are satisfied: