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Proving that compact Hausdorff groups are cofiltered limits of compact Lie groups
What is the easiest way to show that a compact hausdorff topological group is a closed subgroup of a product of finite dimensional Lie groups?
Here are the relevant definitions:
Definition: (compact ...
user531936
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Can the degree of $k$-nilpotence of a simple simply connected compact Lie group be in $(0,1)$?
Let $G$ be a simple (i.e. every proper normal subgroup is discrete) simply connected compact Lie group. Define the degree of $k$-nilpotence of $G$ to be the Haar measure of the set
$$\{(x_1,\dotsc,x_{...
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