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I am looking at Chapter IX (Compact Real Lie Groups), §4, Exercise 8. 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), I have tried and failed to ascertain:

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

I am looking at Chapter IX (Compact Real Lie Groups), §4, Exercise 8 (translation). 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), I have tried and failed to ascertain:

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