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How many topologically distinct metrizations of countable set are there? One can find countably many different ones by arranging points on a plane for example. Are there more than that? How would one approach this?

Radost Waszkiewicz
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  • Technically, arranging points in the plane may still induce the same topology (discrete, for instance). –  Apr 15 '19 at 12:51
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    I'm aware of that. You can get distinct topologies by having different number of accumulation points for instance. That's why I'm asking for topologically distinct not just metrically – Radost Waszkiewicz Apr 15 '19 at 12:53
  • Well spotted @YuiTo Cheng. More of a special case than duplicate, still solves the problem. :) – Radost Waszkiewicz Apr 15 '19 at 13:39

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