Baire space but not locally compact

Question

I need an example that is a Baire space but not locally compact. I think, $\mathbb{R}^ \mathbb{R}$ is such an example.

$\mathbb{R}^ \mathbb{R}$ is not locally compact. But I could not proof that it is a Baire space. could you give me any hint? where can I find the proof?

thanks

Answer 1

What do you mean by $R^R$? I haven't seen this notation. As to an example, think of a manifold and apply the Baire Category Theorem.

Answer 2

Any infinite-dimensional Banach space.