What do you mean with closure properties? These sets of formulas are all closed under boolean operations. LTL is complete with respect to the first order theory of linear orders, i.e., LTL = LO1; and that is also known as the non-counting fragment of the omega-automata. So, for LTL, there are a lot of equivalent formulations know. CTL is a bit ad hoc defined and does not have such strong equivalences, but CTL* inherits those from LTL for branching time, i.e., tree automata and second order monadic logic with many successors.