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Topology

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Facts About First Countability

TOPO-L7JQBW

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

Which of the following is necessarily TRUE?

A

$X$ has countable cardinality.

B

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

C

$(X,\tau)$ is separable.

D

$\tau$ is a topology generated some metric.

E

None of the above need be true.