Solutions and Remarks for Homework                 Sec 1.6, page 35
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#1.  Let z_1 be an arbitrary point in D={z: |z-z_0|< \rho}.
     Then, r = \rhi - |z_0 - z_1| > 0.  Let R=r/2 and consider
     the disk D* = {z: |z-z_1|<R}.  Since, the distance of any
     point in D* from z_1 is less than R, and R<r, we can conclude
     that D* is contained in D.  Hence, by def D is an open set.

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#14. Let D be a closed set and z* be an accumulation point of D. 
     We need to show that z* is a member of D.  If
     z* is in the interior of D or on the boundary, then we are done.
     So, assume that z* is neither.  Then, it is easy to show that
     z* can not be an accumulation point of D.  A contradiction.