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Jan 27, 2023 at 17:13 history edited LSpice CC BY-SA 4.0
Typo
Jan 27, 2023 at 16:15 comment added YCor @BenMcKay no, it's false. If $S$ is semisimple with infinite center, it can be made dense in a larger connected Lie group (namely, fix a dense embedding $f$ of $Z(S)$ into the circle $C$ and mod out $S\times C$ by the graph of $f$).
Jan 27, 2023 at 15:27 vote accept Pablo Lessa
Jan 27, 2023 at 15:23 comment added Ben McKay I think that the paper of Goto mentioned in the question proves that semisimple connected immersed Lie subgroups are closed.
Jan 27, 2023 at 15:16 history answered YCor CC BY-SA 4.0