= Compact generation does not imply local compactness
The compact set $K=\{0\}\cup\{1/n!:n\geq1\}$ generates the additive group $\mathbb Q$, since every positive integer denominator divides some factorial. With its usual topology, $\mathbb Q$ is metrizable and is not locally compact. Nor can it have a nonzero <Haar measure> finite on compact sets: invariance gives equal masses to all singletons; a positive singleton mass makes $K$ have infinite mass, whereas zero singleton masses make the countable group have zero total mass.
// Target: analysis.bigb
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