Answer
a) Yes, Open
b) Yes, Connected Set
c) Yes, Simply connected set
Work Step by Step
a) For the open set, the region should not contain any boundary point. In the given set, we have $0\lt y\lt 3$ , which does not contain any boundary point. Thus, the set is open.
b) For the connected set, any two points in the region $D$ can be connected by a path that lies entirely in $D$. Thus, the set is connected.
c) For the simply connected set, the region must not have any holes or be divided into two parts. The given set satisfies this definition, thus, the set is simply connected.
