Distance and Measurement in Domain Theory

We investigate the notion of distance on domains. In particular, we show that measurement is a fundamental concept underlying partial metrics by proving that a domain in its Scott topology is partially metrizable only if it admits a measurement. Conversely, the natural notion of a distance associated with a measurement not only yields meaningful partial metrics on domains of essential importance in computation, such as IR, Σ∞ and Pω, it also serves as a useful theoretical device by allowing one to establish the existence of partial metrics on arbitrary ω-continuous dcpo’s.