Need to know what this theorem is asking 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?
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.
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.