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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
##### Keywords:
sober topological space; Scott topology; weak topology
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