# could I get help with a paper about topology?

I am referring to a paper which is over here:

www.scipub.org/fulltext/jcs/jcs410879-889.pdf

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.

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if I could see a proof of Proposition 2, that would help a lot (or some idea how to prove it) - because then I would be able to understand what they mean in the proposition itself. –  normvector Feb 6 '11 at 23:29
In line with the title of the question, perhaps one of the topologists who frequent this site would like to help out by suggesting a more interesting "topology paper" to read? I agree with Jim Belk that there's not so much content in this one. –  Pete L. Clark Feb 7 '11 at 5:46

Since $\mathrm{Ob}$ is assumed to be finite (first page, 2nd column), you do not need to worry about infinite unions.