I am looking at Chapter IX (Compact Real Lie Groups), §4, [Exercise 8](//books.google.com/books?id=oCO0xOzNLhAC&ots=GAtbTG6jgI&pg=PA399&dq=%22complex+subspaces%22). Given a complex subspace $\mathfrak p$ in the complexification $\mathfrak g_{\mathbf C}$ of some $\mathfrak g$, they start talking about
$$
\overline{\mathfrak p}.
$$
While I think I know what that bar means (conjugation of $\mathfrak g_{\mathbf C}$ w.r.t. $\mathfrak g$ as in e.g. [Knapp](//books.google.com/books?id=J8EGCAAAQBAJ&ots=RSYddmrOIL&pg=PA209&dq=%22Thus+let+bar+denote%22)), I have tried and failed to ascertain:

> **Q:** Is this notation out of nowhere, or actually introduced some place in the book (or treatise)?