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Distance and Measurement in Domain Theory

✍ Scribed by Paweł Waszkiewicz

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
199 KB
Volume
45
Category
Article
ISSN
1571-0661

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✦ Synopsis

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.

Waszkiewicz

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