I'm searching for a good reference that prove the descending chain propriety for compact Lie groups (i.e. every sequence $K\_1\supset K\_2\supset...$ of closed subgroups $K\_i$ of $G$ is eventually constant).


Thank you!



Descending chain property for compact Lie goups
Am I missing something, or does it follow from the fact that a closed subgroup is either a union of connected components or of lower dimension, and by compactness the number of connected components is finite, while by Lieness, the dimension is finite?


