Example 1.25.  Let  .  (c) Find boundary of  S.

Explore Solution 1.25 (c).  Find the boundary of S.

If   is any point on the unit circle, then any -neighborhood of    will contain the point  , which belongs to  S,  and    which does not belong to  S.  It follows that the boundary of  S  is the unit circle  .  

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