Some results on poset models consisting of compact saturated subsets. (English) Zbl 07513473
Jung, Achim (ed.) et al., Proceedings of the 8th international symposium on domain theory and its applications, ISDT 2019, Yangzhou, China, June 14–17, 2019. Amsterdam: Elsevier. Electron. Notes Theor. Comput. Sci. 345, 77-85 (2019).
Summary: Given a topological space \(X\), the set \(\mathcal{Q}(X)\) of all nonempty saturated compact subsets of \(X\) is a poset with respect to the reverse inclusion order. The posets of the form \(\mathcal{Q}(X)\) play important roles in several aspects of domain theory. In this paper, we investigate some further properties of such posets, in particular their links to the dcpo models of \(T_1\) topological spaces.
For the entire collection see [Zbl 1420.68011].
For the entire collection see [Zbl 1420.68011].
MSC:
| 68Q55 | Semantics in the theory of computing |
| 06B35 | Continuous lattices and posets, applications |
| 54D10 | Lower separation axioms (\(T_0\)–\(T_3\), etc.) |
| 54F05 | Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces |
Keywords:
Scott topology; maximal point space; dcpo model; compact saturated subset; K-filter defined space; \(k\)-spaceReferences:
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