Definition:Real Interval/Definition 2

Definition
A real interval is a subset of $\R$ that is one of the following real interval types:
 * closed bounded interval
 * open bounded interval
 * left half-open bounded interval
 * right half-open bounded interval
 * closed and bounded on the right, also known as a closed unbounded below real interval
 * open and bounded on the right, also known as an open unbounded below real interval
 * closed and bounded on the left, also known as a closed unbounded above real interval
 * open and bounded on the left, also known as an open unbounded above real interval
 * unbounded interval without endpoints

Also see

 * Equivalence of Definitions of Real Interval