Calling close() on the Connection object should cause closing of all Statement objects created on this connection

From very beginning C/C++ impements JDBC-like interface, and JDBC specs say "All Statement objects created from a given
Connection object will be closed when the close method for the Connection
object is called.". I guess it makes sense to follow JDBC specs as much, as possible, since in general this is well thought thru DB access interface specification. This particular case looks sensible.