The easy version of this question is: when a topological group is a Lie group? ]]>

Just noticed that the next post appears to answer the question in the affirmative,

“With this approach, one can avoid any appeal to von Neumann’s theorem and Cartan’s theorem (discussed in this post), or the Kuranishi-Gleason extension theorem (discussed in this post).”

W.

]]>“By a result of Kakutani and Gleason (discussed here), this implies that is itself a Lie group, as required.”

The corresponding blogpost seems (?) to suggest the proof goes back to Kuranishi and Gleason:

“This result can be obtained by combining a result of Kuranishi with a result of Gleason;”

Is this a typo?

*[Corrected, thanks – T.]*