The formal ball model for -categories
2010 ◽
Vol 21
(1)
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pp. 41-64
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Keyword(s):
We generalise the construction of the formal ball model for metric spaces due to A. Edalat and R. Heckmann in order to obtain computational models for separated-categories. We fully describe-categories that are(a)Yoneda complete(b)continuous Yoneda completevia their formal ball models. Our results yield solutions to two open problems in the theory of quasi-metric spaces by showing that:(a)a quasi-metric spaceXis Yoneda complete if and only if its formal ball model is a dcpo, and(b)a quasi-metric spaceXis continuous and Yoneda complete if and only if its formal ball modelBXis a domain that admits a simple characterisation of approximation.
1994 ◽
Vol 144
◽
pp. 431-434
Keyword(s):
1979 ◽
Vol 44
◽
pp. 357-372
Keyword(s):
1977 ◽
Vol 35
◽
pp. 210-211
Keyword(s):
1970 ◽
Vol 28
◽
pp. 542-543
Keyword(s):
1967 ◽
Vol 25
◽
pp. 170-171