The horofunction compactification ofℓ1-products of metric spaces

We study the horofunction compactification of the l^1-product of proper geodesic metric spaces. We provide a complete characterisation of the horofunction compactification of the product space in terms of the horofunctions of the constituent spaces, and provide a complete characterisa- tion of the Busemann points in terms of the Busemann points of the constituent spaces. We also identify the parts of the horofunction boundary and the detour distance. The results are applied to show that the horofunction compactification of the l^1-product of finite dimensional normed spaces with polyhedral or smooth unit balls is naturally homeomorphic to the closed dual unit ball.