  We take the abstract basis approach to classical domain theory and extend it
to quantitative domains. In doing so, we provide dual characterisations of
distance domains (some new even in the classical case) as well as unifying and
extending previous formal ball dualities, namely the Kostanek-Waszkiewicz and
Romaguero-Valero theorems. In passing, we also characterise hemimetric spaces
that admit a hemimetric Smyth completion.

General Topology