Abstract
This paper deals with the relation between lattice-equivalence and some separation axioms.
We are concerned with two questions:
The first one is to characterize topological spaces X such that X and F(X) are lattice equivalent for some covariant functors F from TOP to itself.
In the second question, it is proved that T-(0,T-2), T-(S,T-D), T-(S,T-1) and T-(0,T-3 1/2) are lattice-invariant properties but S, T-(0,T-1), T-(0,T-S), T-(1,T-2), T-(1,T-S), T-(1,T-3 1/2) and T-(0,T-D) are not.