## Definition 5.3.4: Totally Disconnected

A set

**S**is called**totally disconnected**if for each distinct*x, y*there exist disjoint open set**S****U**and**V**such that*x*,**U***y*, and (**V****U****S**) (**V****S**) =**S**.
A set **S** is called **totally disconnected** if for
each distinct
*x, y ***S**
there exist disjoint open set **U** and **V** such that
*x ***U**,
*y ***V**,
and
(**U** **S**)
(**V**
**S**) = **S**.