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For any integer ''q'' ≥ 2, the topology on the group G='''Z'''<sub>''q''</sub><sup>ω</sup> (the countable direct sum) is discrete. Although the [[Pontrjagin dual]] Γ is also '''Z'''<sub>''q''</sub><sup>ω</sup>, the topology of Γ is compact. One can see that Γ is totally disconnected and perfect - thus it is homeomorphic to the Cantor set. It is easiest to write out the homeomorphism explicitly in the case ''q''=2. (See Rudin 1962 p 40.)
The [[geometric mean]] of the Cantor set is approximately 0.274974.<ref>
===Measure and probability===
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