Is there any description known of the Hausdorff topologies on $\mathbb{Q}$ compatible with the group operations?
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$\begingroup$ There are $2^{2^{Card(\mathbb{Q})}}$ distinct field topologies on $\mathbb{Q}$, not so much describable. See mathoverflow.net/q/106448/6451 . See also Zelenyuk, Protasov, Topologies on abelian groups, Mathematics of the USSR-Izvestiya(1991),37(2):445 $\endgroup$– BS.Commented Nov 25, 2014 at 15:47
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