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Jun 21, 2017 at 21:17 comment added Ashutosh Davies' proof does not use CH. The reference is Davies, Roy O., Covering the plane with denumerably many curves, J. London Math. Soc. 38 1963, 433–438
Jun 21, 2017 at 20:04 comment added Julian Newman (Okay, I now see that the answer given there assumes CH, but that's okay.)
Jun 21, 2017 at 13:02 comment added Ashutosh See math.stackexchange.com/questions/836856/…
Jun 20, 2017 at 15:57 history asked Julian Newman CC BY-SA 3.0