Rectangles

Why

We want to talk about which sets of points correspond to rectangles in the real plane.

Definition

A rectangle is the cartesian product of two intervals. We clarify in the case that the intervals are either closed or open. In these cases we call it an open rectangle or a closed rectangle. If both intervals are half-open on the left or right we call it a left-open rectangle or right-open rectangle respectively.

Notation

Let $\ci{x_1, x_2},\ci{y_1,y_2}\in\R ^2$. Then $\ci{x_1, x_2} \times \ci{y_1,y_2}$ is a closed rectangle.