  : In studies of discrete structures, functions are frequently used that
express proximity, but are not metrics. We consider a class of such functions
that is characterized by a normalization condition and an inequality that plays
the same role as the triangle inequality does for metrics. We show that the
introduced functions, named $\Sigma$-proximities, are in a definite sense dual
to metrics: there exists a natural one-to-one correspondence between metrics
and $\Sigma$-proximities defined on the same finite set; in contrast to
metrics, $\Sigma$-proximities measure {\it comparative} proximity; the closer
the objects, the greater the $\Sigma$-proximity; diagonal entries of the
$\Sigma$-proximity matrix characterize the ``centrality'' of elements. The
results are extended to arbitrary infinite sets.
