Colebunders, E.; De Wachter, S.; Lowen, B. Intrinsic approach spaces on domains. (English) Zbl 1231.06012 Topology Appl. 158, No. 17, 2343-2355 (2011). Summary: The paper is a contribution to quantifiability of domains. We show that every domain \(X\), regardless of cardinality conditions for a domain bases, is quantifiable in the sense that there exists an approach structure on \(X\) [R. Lowen, Approach spaces: the missing link in the topology-uniformity-metric triad. Oxford: Clarendon Press (1997; Zbl 0891.54001)] defined by means of a gauge of quasi-metrics, inducing the Scott topology. We get weightability for free and in the case of an algebraic domain satisfying the Lawson condition [J. Lawson, Math. Struct. Comput. Sci. 7, No. 5, 543–555 (1997; Zbl 0985.54025)] a quantifying approach space can be obtained with a weight satisfying the kernel condition. Cited in 8 Documents MSC: 06B35 Continuous lattices and posets, applications 06F30 Ordered topological structures 54A05 Topological spaces and generalizations (closure spaces, etc.) 54B30 Categorical methods in general topology Keywords:continuous dcpo; weightable quasi-metric; approach space; Scott topology; quantifiability of domains; kernel condition Citations:Zbl 0891.54001; Zbl 0985.54025 PDFBibTeX XMLCite \textit{E. Colebunders} et al., Topology Appl. 158, No. 17, 2343--2355 (2011; Zbl 1231.06012) Full Text: DOI References: [1] Adámek, J.; Herrlich, H.; Strecker, G. E., Abstract and Concrete Categories, Pure Appl. Math. (New York) (1990), John Wiley & Sons Inc.: John Wiley & Sons Inc. New York · Zbl 0695.18001 [2] Claes, V., Initially dense objects for metrically generated theories, Topology Appl., 156, 2082-2087 (2009) · Zbl 1185.54010 [3] Edalat, A.; Heckmann, R., A computational model for metric spaces, Theoret. Comput. Sci., 193, 53-73 (1998) · Zbl 1011.54026 [4] Garcia-Raffi, L. M.; Romaguera, S.; Schellekens, M. P., Applications of the complexity space to the general probabilistic divide and conquer algorithms, J. Math. Anal. Appl., 348, 1, 346-355 (2008) · Zbl 1149.68080 [5] Gierz, G.; Hofmann, K. H.; Keimel, K.; Lawson, J. D.; Mislove, M.; Scott, D. S., Continuous Lattices and Domains, Encyclopedia Math. Appl., vol. 93 (2003), Cambridge University Press [6] Künzi, H.-P.; Vajner, V., Weighted quasi-metrics, (Ann. New York Acad. Sci., vol. 728 (1994)), 64-77 · Zbl 0915.54023 [7] Künzi, H.-P., Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology, (Aull, C. E.; Lowen, R., Handbook of the History of General Topology, vol. 3 (2001), Kluwer Ac. Publ.), 853-968 · Zbl 1002.54002 [8] Lawson, J. D., Spaces of maximal points, Math. Structures Comput. Sci., 7, 5, 543-555 (1997) · Zbl 0985.54025 [9] Lowen, R., Approach Spaces, Oxford Math. Monogr. (1997), Oxford University Press: Oxford University Press New York · Zbl 0912.46009 [10] Matthews, S. G., Partial metric topology, (Proceedings of the 8th Summer Conference on General Topology and Applications. Proceedings of the 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., vol. 728 (1994)), 183-197 · Zbl 0911.54025 [11] Plotkin, G., \(T^\omega\) as a universal domain, J. Comput. System Sci., 17, 209-230 (1978) · Zbl 0419.03007 [12] Schellekens, M. P., A characterization of partial metrizability: domains are quantifiable, Theoret. Comput. Sci., 305, 1-3, 409-432 (2003) · Zbl 1043.54011 [13] Waszkiewicz, P., Distance and measurement in domain theory, Electron. Notes Theor. Comput. Sci., 45, 1-15 (2001) [14] Waszkiewicz, P., Quantitative continuous domains, Appl. Categ. Structures, 11, 41-67 (2003) · Zbl 1030.06005 [15] Yinbin, L.; Maokang, L., A proof of Plotkinʼs Conjecture, Fund. Inform., 92, 301-306 (2009) · Zbl 1192.06006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.