Given a set X={a,b,c} is the following subset a topology for X:

{ X,{a},{b},{a,b},{a,c},{empty set} } ?

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- Nov 5th 2009, 04:40 AMbigdoggytopology?
Given a set X={a,b,c} is the following subset a topology for X:

{ X,{a},{b},{a,b},{a,c},{empty set} } ? - Nov 5th 2009, 05:01 AMHallsofIvy
Does it satisfy the criteria for a topology?

1) Does it include the empty set?

Yes.

2) Does it include X itself?

Yes.

3) If it includes set U and V does it include $\displaystyle U\cap V$.

Since there are only 6 sets here, you could just check every possible intersection- yes, it does,.

4) Are all possible unions of members of the collection in the collection?

Again, there are only a finite number of unions to try- yes, it does.

So this is, in fact, a topology for X.