1. One convex set which is Cartesian product of nonregular convex polygons is used instead of the other convex set which is Cartesian product of regular polygons. 采用不规则凸多边形的笛卡儿积构成的凸集代替正多边形的笛卡儿积构成的凸集，前者比后者更紧凑。
2. The lexicographical order on the Cartesian product of a set of totally ordered sets indexed by an ordinal, is itself a total order. 在用一个序数索引的那些全序集合的笛卡尔积的一个集合上的词典序自身是全序。
3. and proves that Cartesian countable product of the B_*-spaces must have B_*-metrization. This is an important result on the B_*-axiom. 即B_*-空间的笛卡儿可数积可以有B_*-度量化，这是一个关于B_*-空间的重要结果。
4. My arguments in this chapter have been in a Cartesian spirit. 我的论证，在这一章，是在笛卡尔的精神中的。
5. My arguments in this chapter have been in a Cartesian spirit. 我在这一章中所论证的是笛卡尔式精神。
