Which collections are topologies?

[uncledub]

Homework Statement

Which of the following collections are topologies for the real numbers? If a collection is not a topology for the real numbers, explain why not.

Homework Equations

{R,empty set, (1,3), (2,4)}

The Attempt at a Solution

Not a topology because (1,3) U (2,4) = (1,4)
(1,4) is not in the collection

My hang up on this problem lies in the fact that (1,4) is in the real numbers. But I think all of my answers have to be a member of my original collection.

 

[fzero]

But I think all of my answers have to be a member of my original collection.

This is true. Have you examined the intersection of the sets as well?

 

[uncledub]

I stopped there because I assumed I could stop after I found it was not true. On my other problems I did examine the intersections as well.

Thank you.