Horofunction Compactifications and Duality

Abstract We study the global topology and geometry of horofunction compactification classes symmetric spaces under Finsler distances in three settings: bounded domains form $$B=B_1\times \cdots \times B_r$$ B = 1 × ⋯ r , where $$B_i$$ i is an open Euclidean ball $${\mathbb {C}}^{n_i}$$ C n with Kobayashi distance, cones Hilbert Jordan algebras spectral norm. For these we show, that naturally homeomorphic to closed unit dual norm metric tangent space at basepoint. In each case give explicit homeomorphism. finite dimensional normed link between was suggested by Kapovich Leeb, which confirm for Our results also show this duality phenomenon not only occurs spaces, but a variety noncompact type invariant metrics.