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8.63 (1982)

Solved

Suppose that the space of all closed subgroups of a locally compact group $G$ is $\sigma$-compact in the $E$-topology. Is it true that the set of closed non-compact subgroups of $G$ is at most countable?

Contributor: I. V. Protasov

Progress

Yes, it is (A. G. Piskunov, Ukrain. J. Math., 40 (1988), 679–683).

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