Name
Abstract | ||
|---|---|---|
A remarkable result due to Kou, Liu u0026 Luo states that the condition of continuity for a dcpo can be split into quasi-continuity and meet-continuity. Their argument contained a gap, however, which is probably why the authors of the monograph Continuous Lattices and Domains used a different (and fairly sophisticated) sequence of lemmas in order to establish the result. In this note we show that by considering the Stone dual, that is, the lattice of Scott-open subsets, a straightforward proof may be given. We do this by showing that a complete lattice is prime-continuous if and only if it is join-continuous and hypercontinuous. A pleasant side effect of this approach is that the characterisation of continuity by Kou, Liu u0026 Luo also holds for posets, not just dcpos. |
Year | Venue | Field |
|---|---|---|
2016 | arXiv: Logic in Computer Science | Prime (order theory),Discrete mathematics,Lattice (order),If and only if,Complete partial order,Complete lattice,Mathematics,Lemma (mathematics) |
DocType | Volume | Citations |
Journal | abs/1607.01886 | 0 |
PageRank | References | Authors |
0.34 | 2 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Weng Kin Ho | 1 | 23 | 5.41 |
| Achim Jung | 2 | 111 | 13.07 |
| Dongsheng Zhao | 3 | 64 | 6.88 |