An Intrinsic Approach To The Boundaries of X

Abstract

It is well-known that any symmetric space X of non-compact type can be realized as the space So of maximal compact subgroups by associating with g · o its isotropy subgroup gKg^-1. The space S of closed subgroups of G is compact in the topology of Hausdorff convergence on the compact subsets of G. As a result, the closure $\overline {{S_0}}$ is a compactification of X.