When X is a CAT(0)-space, one defines a boundary dX, which is endowed
with the so-called cone topology. This applies in particular when X is
the Bruhat-Tits building of a semi-simple group over an ultrametric
local field F. Then dX is a vectorial building, the cone topology is a
new topology and the union of X and dX is compact. When X is a masure
(=hovel) associated e.g. to a Kac-Moody group G over F, one finds at
infinity of X the twin buildings dX_+, dX_- of G. I shall explain the
definition and properties of the cone topology on the set of chambers of
dX_+, dX_- .