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Why $\mathbb{Z}$ (group of integer numbers) with $p$-adic topology is a countable precompact metric group with a linear topology?

Note : Call a topological group $G$ linear (and its topology a linear group topology) if $G$ has a base of $e$ formed by open subgroups of $G$.

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    Which of the 5 properties do you not believe? Only prcompact?2012-10-05
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    yes,just precompact.2012-10-05

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