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## Homework Statement

Is the space [tex] X=\mathbb{R\backslash}\left\{ a+b\sqrt{2}\::\: a,b\in\mathbb{Q}\right\} [/tex] locally compact?

## Homework Equations

According to the baire theorem, in a locally compact hausdorf space, the intersection of dense open sets is dense.

## The Attempt at a Solution

I'm leaning for a no here and want to show a violation of the baire theorem. I'm not sure how to go about constucting my dense sets because I am not sure what is dense in this subset.

Thanks

Tal