Metrizability of a compact abelian group
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Problem VII.9.10 from Conway J.B. "A Course in Functional Analysis" [Con07]More problems in Section VII.9 "The Group Algebra of a Locally Compact Abelian Group"
If is a compact abelian group, show that is metrizable if and only if is countable.
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Origin: Stated according to the original source
References
[Con07] Conway J.B. A Course in Functional Analysis. 2nd ed., Springer, 2007.