| Autor: |
Weng Kin Ho, Jean Goubault-Larrecq, Achim Jung, Xiaoyong Xi |
| Jazyk: |
angličtina |
| Rok vydání: |
2018 |
| Předmět: |
|
| Zdroj: |
Logical Methods in Computer Science, Vol Volume 14, Issue 1 (2018) |
| Druh dokumentu: |
article |
| ISSN: |
1860-5974 |
| DOI: |
10.23638/LMCS-14(1:7)2018 |
| Popis: |
Given a poset $P$, the set, $\Gamma(P)$, of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory $\mathbf{C}$ of $\mathbf{Pos}_d$ (the category of posets and Scott-continuous maps) is said to be $\Gamma$-faithful if for any posets $P$ and $Q$ in $\mathbf{C}$, $\Gamma(P) \cong \Gamma(Q)$ implies $P \cong Q$. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are $\Gamma$-faithful, while $\mathbf{Pos}_d$ is not. Ho & Zhao (2009) asked whether the category $\mathbf{DCPO}$ of dcpos is $\Gamma$-faithful. In this paper, we answer this question in the negative by exhibiting a counterexample. To achieve this, we introduce a new subcategory of dcpos which is $\Gamma$-faithful. This subcategory subsumes all currently known $\Gamma$-faithful subcategories. With this new concept in mind, we construct the desired counterexample which relies heavily on Johnstone's famous dcpo which is not sober in its Scott topology. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
|
