  Diversities have been recently introduced as a generalization of metrics for
which a rich tight span theory could be stated. In this work we take up a
number of questions about hyperconvexity, diversities and fixed points of
nonexpansive mappings. Most of these questions are motivated by the study of
the connection between a hyperconvex diversity and its induced metric space for
which we provide some answers. Examples are given, for instance, showing that
such a metric space need not be hyperconvex but still we prove, as our main
result, that they enjoy the fixed point property for nonexpansive mappings
provided the diversity is bounded and that this boundedness condition cannot be
transferred from the diversity to the induced metric space.
