cartesian product in a sentence

Examples

1. We wish to show that the cartesian product of these sets is nonempty.
2. The graph of a function is contained in a Cartesian product of sets.
3. The Cartesian product of an infinite set and a nonempty set is infinite.
4. Higher order prismatic polytopes also exist as cartesian products of any two polytopes.
5. The graph of an empty function is a subset of the Cartesian product.
6. The cartesian product of two curves also provides examples.
7. The Cartesian product of two circles may be taken to obtain a duocylinder.
8. Another construction of is the Cartesian product of two-vertex complete graphs.
9. Some complex polytopes can be represented as Cartesian products.
10. Can you imagine the torus as a cartesian product in the manner described?