a) Yes b) Yes c) Yes
Work Step by Step
a) The region should not have any boundary point in order to get the open set . There is no boundary point in the given set $0\lt y\lt 3$.So, the set is 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. c) The region should not contain any holes or does not divided into two parts In order to get the simply connected set.So, the given set $0\lt y\lt 3$ satisfies this condition.So, the set is simply connected.