Chapter 16 - Vector Calculus - 16.3 The Fundamental Theorem for Line Integrals - 16.3 Exercises - Page 1135: 33

a) No b) Yes c) Yes

a) The region should not have any boundary point in order to get the open set. We can see that when we draw a disk for the given set, it does not completely lie inside the region $D$.So, the set is not open. b)Any two points in the region domain $D$ should be connected to a straight segment path In order to get the connected set that lies entirely inside the domain $D$. So, the set is connected.From the given points when we draw a path , it connects the two points in the $D$. c) The region should not contain any holes or does not divided into two parts In order to get the simply connected set. In the given points, we can see that the path connecting the two points lie inside the given set and this implies that the set is simply connected.