论文标题
集合在主教集理论中完全通过功能分开
Sets completely separated by functions in Bishop Set Theory
论文作者
论文摘要
在主教集理论中，我们研究了主教的集合理论，我们研究了所谓的完全分开的集合，该集合配备了由给定的真实价值函数引起的正面不平等概念。我们介绍了一个全球完全分开的索引完全分开的集合的概念，并描述了其Sigma-和pi-stet。还介绍了给定集合上的自由完全分开的集合。给出了经典的Stone-čech定理的纯粹的理论版本和完全定期空间的Tychonoff定理，用功能空间和完全分离的集合代替了拓扑空间。
Within Bishop Set Theory, a reconstruction of Bishop's theory of sets, we study the so-called completely separated sets, that is sets equipped with a positive notion of an inequality, induced by a given set of real-valued functions. We introduce the notion of a global family of completely separated sets over an index-completely separated set, and we describe its Sigma- and Pi-set. The free completely separated set on a given set is also presented. Purely set-theoretic versions of the classical Stone-Čech theorem and the Tychonoff embedding theorem for completely regular spaces are given, replacing topological spaces with function spaces and completely regular spaces with completely separated sets.
