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May 13, 2017 at 12:43 comment added Igor Belegradek That every compact Lie group has at most countably many conjugacy classes of closed subgroups is proved in Corollary 1.7.27 [Palais, Memoirs AMS, The classification of $G$-spaces, 1960], see p.39 at vmm.math.uci.edu/PalaisPapers/ClassificationOfG-Spaces.pdf.
Mar 28, 2017 at 6:50 history answered YCor CC BY-SA 3.0