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Let $X=\{2,3,4,\ldots\}$ and let the open sets be the set of unions of sets of the form $U_n=\{k\in X : k|n\}$.

Is there a name for this space? Google is not helping me.

Henno Brandsma
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1 Answers1

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This is called the Divisor Topology in Steen/Seebach's Counterexamples in Topology, Example 57 on pp. 79-80 of the 1978 2nd edition (same location in the 1995 Dover reprint of the 2nd edition). Googling, I see there is a Wikipedia article for the Divisor Topology.

Dave L. Renfro
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