A

set is clopen if it is simultaneously

open and

closed in a

topological space.

**Example**: Members of the

base *B* = { |

*x*,

*r*):

*x*,

*r* in

**R**,

*x* <

*r*,

*r* is

rational } for the Sorgenfrey line are clopen

with respect to the

topology generated by

*B*.

**Example**: Given a set

**X**,

**X** and

**Ø** are always clopen in

**X**. If a subset

**U** of

**X** is clopen, its complement,

**X**/

**U**, is also clopen.

*what a fun word to say*