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Let $(X,\tau)$ be a second countable topological space.

Which of the following are necessarily TRUE?

Select ALL that apply.

A

$X$ has countable cardinality.

B

$(X,\tau)$ is first countable.

C

$(X,\tau)$ is separable.

D

$\tau$ is a topology generated a metric.

E

$\tau$ has countable cardinality.

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