## Definition 5.1.1: Open and Closed Sets

A set

**U****R**is called**open**, if for each*x*there exists and**U***> 0*such that the interval*( x - , x + )*is contained in**U**. Such an interval is often called an**-neighborhood**of*x*, or simply a neighborhood of*x*.
A set **F** is called **closed** if the complement of
**F**, **R** \ **F**, is open.