The title pretty much sums up the question: Suppose $G$ is a compact semisimple Lie group with center $Z$, The question is if $G/Z$ is always compact? or, under which conditions will it be compact?
2026-03-30 00:05:23.1774829123
If G is a compact semisimple Lie group and Z is its center, is G/Z always compact?
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Any quotient of any compact topological group is compact, because the image of a compact set under a continuous map is compact.