underlying decompositions where there are induced surjectionssince we must have . Under the inverse limit definition of the profinite integers, we have the isomorphismwith the direct product of p-adic integers. Explicitly, the isomorphism is bywhere ranges over all prime-power factors of ; that is, for some different prime numbers .

Relations

Topological properties

The set of profinite integers has an induced topology in which it is a compact Hausdorff space

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