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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

1 Answer 1

up vote 1 down vote accepted

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

You are correct about the meaning of proposition 2.

(By the way, it seems to me to be a very trivial example of a topology, and I'm a bit skeptical that the paper will be able to make anything interesting out of it.)

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