  It is observed that a natural analog of the Hahn-Banach theorem is valid for
metric functionals but fails for horofunctions. Several statements of the
existence of invariant metric functionals for individual isometries and
1-Lipschitz maps are proved. Various other definitions, examples and facts are
pointed out related to this topic. In particular it is shown that the metric
(horofunction) boundary of every infinite Cayley graphs contains at least two
points.
