I am trying to do the following exercise from Hirsch's Differential topology :
The subspace $X=\{f\in C_S^0(\mathbb{R},\mathbb{R}):supp f$ is compact $\}$ is closed but does not have the baire property.
I was able to see that this set is closed by proving that the complement is open. Now how do we prove that this not a baire space ? I mean I guess the idea would be to take dense open sets $\{A_n\}_{n=1}^{\infty}$ such that $\cap_{n=1}^{\infty}A_n$ is not dense in $X$, but I have no clue what dense open sets to consider, I don't even know any good dense open sets in $X$. Does anybody have any suggestions ?
Thanks in advance.