On monotone determined spaces. (English) Zbl 1395.54028
Luo, Mao-Kang (ed.) et al., Proceedings of the 7th international symposium on domain theory and its applications (ISDT), Shijiazhuang, China, June 2–6, 2017. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 333, 63-72 (2017).
Summary: In this paper, we investigate some basic properties, especially categorical properties, of monotone determined spaces. For a topology \(\tau\), we construct a monotone determined topology \(\mathrm{md}(\tau)\). The main results are: (1) for a space \((X, \tau)\), then \(\mathrm{md}(\tau)\) is the weakest monotone determined topology on \(X\) containing \(\tau\); (2) the category \(\mathrm{Top}_{\mathrm{md}}\) of monotone determined spaces with continuous maps is fully co-reflexive in the category Top of all topology spaces with continuous maps; (3) the category \(\mathrm{Top}_{\mathrm{md}}\) is Cartesian closed.
For the entire collection see [Zbl 1376.68012].
For the entire collection see [Zbl 1376.68012].
MSC:
| 54F05 | Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces |
| 06B35 | Continuous lattices and posets, applications |
| 18B30 | Categories of topological spaces and continuous mappings (MSC2010) |
| 18D15 | Closed categories (closed monoidal and Cartesian closed categories, etc.) |
| 54B30 | Categorical methods in general topology |
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