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Topology

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Subspaces, Separability, And Second Countability

TOPO-9YIZYL

Let $(X,\tau)$ be a topological space and $Y\subseteq X$ a subspace of $X$. Which of the following must hold?

Select ALL that apply.

A

If $X$ is separable, then $Y$ is separable.

B

If $X$ is second countable, then $Y$ is second countable.

C

If $X$ is second countable, then $Y$ is separable.

D

If $X$ is separable, then $Y$ is second countable.

E

Nothing can be conlcuded about the separability or second countability of $Y$ from information about $X$ alone.