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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.

MSC:
06B30 Topological lattices
06B35 Continuous lattices and posets, applications
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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