(915, #31) Determine whether or not the following set is (a) open, (b) connected, and (c) simply-connected.

Solution: The set is the yellow shaded region below. It does not include the boundaries, the red and green circles.

1. D is open, around every point in D we can put a disk that lies in D.
2. D is connected, any two points in D can be joined by a path that lies in D.
3. D is not simply not connected, D has a hole.
   

By C.A.H.