I am referring to a paper which is over here:
The paper is not hard to read, but I think notation is rather sloppy.
I am specifically referring page 880, "Materials and Methods" in the beginning. Elementary sets are defined as the equivalence classes of some equivalence relation $A=(Ob,R)$ where $Ob$ is the universe and $R$ is the relation (an approximation space it is called?), and then in turn we define $com(A)$ to be the set of all finite unions of elementary sets (the equivalence relations).
This $com(A)$ is supposed to be a topology, according to the paper, but I don't see why. What about infinite unions? They should also be there.
Another problem... In proposition 2, they mention $\tau_2 \subseteq \tau_1$. Does that mean that the open sets of the second topology should be a subset of the open sets of the first topology?
Like I said, I think notation is rather sloppy there, but I may be misunderstanding something. Any help appreciated.