Properties of domain representations of spaces through dyadic subbases
2016 ◽
Vol 27
(8)
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pp. 1625-1638
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.
2015 ◽
Vol 26
(03)
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pp. 1550032
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2001 ◽
Vol 27
(8)
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pp. 505-512
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1978 ◽
Vol 21
(2)
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pp. 183-186
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1996 ◽
Vol 19
(2)
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pp. 311-316
2013 ◽
Vol 2013
◽
pp. 1-6
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1982 ◽
Vol 91
(3)
◽
pp. 457-458
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