Need to know what this theorem is asking

Question

Theorem Let (Y,$\tau_1$) be a a Subspace of (X,$\tau$) If (X $\tau$) satisfies Second Countable axiom Show (Y,$\tau_1$) does too

My question is this : is this theorem asking us to prove the hereditary of the Second Countable axiom?

Answer 1

It is indeed asking to show that the property “$X$ is second countable “ is hereditary with respect to all subspaces.

Not that it helps with the proof.