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The evenly spaced integer topology is countable, metrizable, and has no isolated points, and hence is homeomorphic to the rationals with the order topology. But what is an explicit construction for this homeomorphism?

This question was asked on MSE but got no answer: https://math.stackexchange.com/q/1849271/52694

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    $\begingroup$ You refer to a certain theorem asserting that such spaces are homeomorphic. Have you read the proof of this theorem? $\endgroup$
    – YCor
    Commented Jul 8, 2016 at 8:15

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