I came up with this question when I drew diagrams to represent the relations among special topological space. I am aware that the answer might be trivial, but I haven’t figure out a way to do it yet.
Given two topological properties $P_1$ and $P_2$ such that $P_1<P_2$($P_1$ implies $P_2$, but does not equal to $P_2$. An example would be “$T_0<T_1$”), is there a topological property $P$ such that $P_1<P<P_2$?(“$<$” is defined as above) Can we define a topology using the class of topological properties?