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Properties of domain representations of spaces through dyadic subbases
Published online by Cambridge University Press: 23 June 2016
Abstract
A dyadic subbase S of a topological space X is a subbase consisting of a countable collection of pairs of open subsets that are exteriors of each other. If a dyadic subbase S is proper, then we can construct a dcpo DS in which X is embedded. We study properties of S with respect to two aspects. (i) Whether the dcpo DS is consistently complete depends on not only S itself but also the enumeration of S. We give a characterization of S that induces the consistent completeness of DS regardless of its enumeration. (ii) If the space X is regular Hausdorff, then X is embedded in the minimal limit set of DS. We construct an example of a Hausdorff but non-regular space with a dyadic subbase S such that the minimal limit set of DS is empty.
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- Information
- Mathematical Structures in Computer Science , Volume 27 , Special Issue 8: Continuity, Computability, Constructivity: From Logic to Algorithms 2013 , December 2017 , pp. 1625 - 1638
- Copyright
- Copyright © Cambridge University Press 2016
References
Blanck, J. (2000). Domain representations of topological spaces. Theoretical Computer Science
247
(1–2), 229–255, Elsevier Science.Google Scholar
Erdős, P. (1934). A theorem of Sylvester and Schur. Journal of London Mathematical Society s1-9
(4), 282–288.Google Scholar
Gianantonio, P. D. (1999). An abstract data type for real numbers. Theoretical Computer Science
221
(1–2), 295–326.Google Scholar
Gierz, G., Hofmann, K. H., Keimel, K., Lauson, J. D., Mislove, M. W. and Scott, D. S. (2003). Continuous lattices and domains. Encyclopedia of Mathematics and its Applications 93, Cambridge University Press.Google Scholar
Ohta, H., Tsuiki, H. and Yamada, S. (2011). Independent subbases and non-redundant codings of separable metrizable spaces. Topology and its Applications
158
(1), 1–14, Elsevier Science.Google Scholar
Plotkin, G. (1978).
$\mathbb{T}^{\omega}$
as a universal domain. Journal of Computer and System Sciences
17
(2), 209–236.Google Scholar
$\mathbb{T}^{\omega}$
as a universal domain. Journal of Computer and System Sciences
17
(2), 209–236.Google ScholarTsuiki, H. (2002). Real number computation through Gray code embedding. Theoretical Computer Science
284
(2)
467–485.Google Scholar
Tsuiki, H. (2004a). Compact metric spaces as minimal-limit sets in domains of bottomed sequences. Mathematical Structures in Computer Science
14
(6)
853–878.Google Scholar
Tsuiki, H. (2004b). Dyadic subbases and efficiency properties of the induced {0, 1, ⊥}ω-representations. Topology Proceedings
28
(2)
673–687.Google Scholar
Tsuiki, H. and Tsukamoto, Y. (2015). Domain representations induced by dyadic subbases. Logical Methods in Computer Science
11
(1)
1–17.Google Scholar