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Topology

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Relationship Between Separability and Second Countability

TOPO-BBJUWK

Which of the following are true statements regarding the relationship between separability and second countability?

Select ALL that apply.

A

Every second countable topological space is separable.

B

Every separable topological space is second countable.

C

Every second countable metric space is separable.

D

Every separable metric space is second countable.

E

Neither second countability nor separability implies the other for arbitrary topological spaces.