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Article1303
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Domains and metric spaces are two central tools for the study of denotational semantics in computer science, but are otherwise very different in many fundamental aspects. A construction that tries to establish links between both paradigms is the
space of formal balls, a continuous poset which can be defined for every metric space and that reflects many of its properties. On the other hand, in order to obtain a broader framework for applications and possible connections to domain theory, generalized ultrametric spaces (gums) have been introduced. In this paper, we employ the space of formal balls as a tool for studying these more general metrics by using
concepts and results from domain theory. It turns out that many properties of the
metric can be characterized via its formal-ball space. Furthermore, we can state new results on the topology of gums as well as two new fixed point theorems, which may be compared to the Prieß-Crampe and Ribenboim theorem, and the Banach fixed point theorem, respectively. Deeper insights into the nature of formal-ball spaces are gained by applying methods from category theory. Our results suggest that, while
being a useful tool for the study of gums, the space of formal balls does not provide the hoped-for general connection to domain theory.
0304-3975
Theoretical Computer Science
Dezember
30--49
Markus Krötzsch <br /> '''[[Article1303|Generalized Ultrametric Spaces in Quantitative Domain Theory]]'''<br />''Theoretical Computer Science'', 368, (1--2), Seiten 30--49, Dezember, 2006<br>([[Article1303|Details]])
Markus Krötzsch<br /> '''[[Article1303/en|Generalized Ultrametric Spaces in Quantitative Domain Theory]]'''<br />''Theoretical Computer Science'', 368, (1--2), pages 30--49, Dezember, 2006<br>([[Article1303/en|Details]])
Markus Krötzsch:<br />Generalized Ultrametric Spaces in Quantitative Domain Theory.<br />Theoretical Computer Science 368 (1--2): S. 30--49. Dezember 2006.
Elsevier
true
Generalized Ultrametric Spaces in Quantitative Domain Theory
Article
368
2006
2453736.5
2015-10-08T13:17:05Z
2457304.0535301
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