Is $\mathbb Z$ with the topology $$\tau=\{U\subset \mathbb{Z} :\mathbb{Z}\setminus U\text{ is finite, or }0\notin U\}$$ compact?
Compactness of the topology $\{U\subset \mathbb{Z} :\mathbb{Z}\setminus U\text{ is finite, or }0\notin U\}$ on $\mathbb{Z}$
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general-topology
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0Hint: What is the complement of an open set containing $0$? – 2017-02-20
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1Ok now i got it – 2017-02-20