Remarks on the Satake compactifications (Q2471449)

This article is about various constructions and realizations of the Satake compactifications of Riemannian symmetric spaces. It has three independent parts. The first one is a simplification, using some old results of the author [Invent. Math. 34, 19--35 (1976; Zbl 0328.22017)], of a construction of the compactifications given by \textit{A.~Borel} and \textit{L.~Ji} [Math. Res. Lett. 9, 725--739 (2002; Zbl 1027.22011)] or \textit{A.~Borel} [ Compactifications of symmetric and locally symmetric spaces. Mathematics: Theory and Applications. Basel: Birkhäuser (2006; Zbl 1100.22001)]. The second one is another construction by directly describing the relative neighborhood systems of boundary points. The third is a realization of the space and its compactification as a bounded domain and its closure in a vector space.