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Bjørn Kjos-Hanssen
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Fractals of dimension zero

Are there any famous examples of fractals, or other closed sets, of cardinality continuum but Hausdorff dimension 0?

I can think of something ad hoc like a Cantor middle $\frac13$ set where the middle $\frac13$ is followed by middle $\frac24$, middle $\frac35$ etc. but I am looking for something natural that's been studied before.

Bjørn Kjos-Hanssen
  • 24.8k
  • 3
  • 58
  • 114