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# The Cofinite Topology is not Hausdorff Watch

1. Hi everyone

I have to prove: "The Cofinite Topology is not Hausdorff provided X is infinite"

Please can someone tell me if this makes sense or if I've completely missed the point with all of this stuff:

Let X = the natural numbers and let

Then There exists neighbourhoods U of x: just simply U = X
And there exists neighbourhoods V of y: just simply V = X

And so U intersect V = X which is non empty

So X is not hausdorff
.

Does that make sense?
2. actually, I can just tell for myself it doesn't
3. Given x, y in X. Pick open neighbourhoods... can you find something in their intersection?

Spoiler:
Show
What is the complement of their intersection?

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Updated: November 27, 2010
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