Mathematicians call a

set **X** in a

topological space "perfect" if

**X** is

closed and every point of

**X** is an

accumulation point of

**X**. For example, any

closed interval on the

real line with nonzero

measure is

perfect, but a

singleton such as { 0 } is closed but not perfect.

Every non-empty perfect set of real numbers is uncountable.