Any compact manifold is sequentially compact, if by "manifold" we understand "second-countable Hausdorff etc." This is because such spaces are metrizable by Urysohn's metrization theorem, and for metrizable spaces compactness and sequential compactness are equivalent. Wikipedia tells me this result was published in 1925.

Any compact manifold is sequentially compact, if by "manifold" we understand "second-countable Hausdorff etc." This is because such spaces are metrizable by Urysohn's metrization theorem, and for metrizable spaces compactness and sequential compactness are equivalent. Wikipedia tells me this result was published in 1925.

Given the time period, though, I would not be surprised if "Lie group" meant "matrix Lie group."