The point pair function pG defined in a domain G⊊Rn
is shown to be a quasi-metric and its other properties are studied. For a
convex domain G⊊Rn, a new intrinsic quasi-metric called
the function wG is introduced. Several sharp results are established for
these two quasi-metrics, and their connection to the triangular ratio metric is
studied.Comment: 18 pages, 1 figur