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

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 $\pi_2$ the projection onto the second factor) be a closed map: do these assumptions imply that Y is compact? (There is no assumption $T_0$, $T_1$ or $T_2$ on $Y$.)

thank you in advance.