Example 1.25.  Let  .  (b) Find the exterior of S.  

Explore Solution 1.25 (b). Find the exterior of S.

If   then a similar argument will produce an -neighborhood of    that lies entirely in the region  ,  hence   is an exterior point of  S.  It follows that the exterior of  S  is the open region  .  

(c) 2006 John H. Mathews, Russell W. Howell