Boltjanskii has constructed
classes of semifield quasi-pseudo-metrics which are adequate to metrize topological
spaces with various separation properties. In this paper we show that his condition
given as adequate for T-0 spaces actually is satisfied by every semifield metric
inducing the topology. On the other hand, we show that the condition he
introduced for T-1 and T-2 spaces is never satisfied by a certain natural semifield
quasi-pseudo-metric related to the usual (or Pervin) quasiuniformity. In this paper we
completely characterize the classes of semifield quasi-pseudo-metrics which are not
only adequate to metrize T-1 and T-2 spaces but actually contain all such metrics
inducing such topologies. Characterizations of R-0 and R-1 inducing metrics will also
be obtained. Applications to quasi-uniform and quasi-gauge spaces will be
made.
