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Topology

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Moderate

Checking Compactness and Separability II

TOPO-BXYPZG

Let $X$ be $[0,1]$ with a topology generated by intervals of the form $(a,b]$.

Which of the following is TRUE?

A

$X$ is compact and separable.

B

$X$ is neither compact nor separable.

C

$X$ is compact but not separable.

D

$X$ is separable but not compact.