This set {(x, y) | 0 is (a) open, (b) connected, and (c) not simply-connected.
(a) Open: This set is open because all points within the set have a neighborhood that is also within the set.
(b) Connected: This set is connected because there is a path between any two points in the set that does not leave the set.
(c) Not simply-connected: This set is not simply-connected because it contains a hole in the center, which is not a simply-connected space.
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