Horofunction Compactification of Finite-Dimensional Normed Spaces and of Symmetric Spaces

Abstract:

In the first part of this thesis we consider the horofunction compactification of finite-dimensional normed real spaces and show that the boundary of the compactification has the shape of the dual unit ball if the norm of the space is polyhedral. We will characterise the sequences converging to some Busemann point and see that only the limiting direction and an eventual parallel shift of the sequence have influence on this Busemann point.
In the second part of the thesis we examine symmetric spaces with Finsler metrics and their horofunction compactification by using the results of the first part and we make a short comparison with the Furstenberg compactification.