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Properties of domain representations of spaces through dyadic subbases

Published online by Cambridge University Press:  23 June 2016

YASUYUKI TSUKAMOTO  and
HIDEKI TSUIKI
YASUYUKI TSUKAMOTO
Affiliation:
Graduate School of Human and Environmental Studies, Kyoto University, Yoshida-nihonmatsu-cho, Sakyo-ku, Kyoto 606-8501, Japan Email: [email protected] and [email protected]
HIDEKI TSUIKI
Affiliation:
Graduate School of Human and Environmental Studies, Kyoto University, Yoshida-nihonmatsu-cho, Sakyo-ku, Kyoto 606-8501, Japan Email: [email protected] and [email protected]
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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.

Type
Paper
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 

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