Example 1.25.  Let  .  (a) Find the interior of S. 

Explore Solution 1.25 (a).  Find the interior of S.

Let   be a point of  S.  Then    so that we can choose  .  If  z  lies in the disk  ,  then  

.  

Hence the -neighborhood of    is contained in  S,  and    is an interior point of  S.  It follows that the interior of  S  is the open unit disk.

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