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# Checking Compactness And Separability

TOPO-JDGEJN

Let $\tau$ be a topology on $\mathbb{R}$ consisting of subsets of $\mathbb{R}$ not containing $0$ as well as subsets with finite complement.

Which of the followings is TRUE?

A

This space is separable but not compact.

B

This space is neither compact nor separable.

C

This space is compact but not separable.

D

This space is both compact and separable,