Remarks on the sobriety of Scott topology and weak topology on posets. (English) Zbl 1069.06002
On a poset \(L\) the Scott topology is considered and generalized to the concept of weak topology (then \(L\) is a weakly Scott topological space). Conditions for these topologies to be sober are studied in the case of \(L\) being a poset, in general being a complete lattice, and being a weakly complete poset.
Reviewer: Bohdan Zelinka (Liberec)
MSC:
| 06B30 | Topological lattices |
| 06B35 | Continuous lattices and posets, applications |
| 54F05 | Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces |
