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

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): Notation and Terminology