Product set/Circle and line/Cylinder/Example

The cylinder (its surface) is the product set of a circle and a line segment.

Let ${}S$ denote a circle (the circumference), and let ${}I$ be a line segment. The circle is a subset of a plane ${}E$, and the line segment is a subset of a line ${}G$, so that for the product sets, we have the relation

${}S\times I\subseteq E\times G\,.$

The product set ${}E\times G$ is the three-dimensional space, and the product set ${}S\times I$ is the surface of a cylinder.