Hi!

I'm wondering if the following can be true:
Let Y be a second countable space and
$\pi_2:Y \times \mathbb{R}\rightarrow\mathbb{R}$ ($\mathbb{R}$ with its usual topology and
$\pi_2$ is the projection onto the second factor)
is a closed map, does these assumptions imply
that Y is compact? (there is no assumprion $T_0$, $T_1$ or $T_2$ on $Y$)

thank you in advance