Discontinuity of Meets and Joins

This paper concerns examples of complete lattices L for which binary meet, or join, from L × L to L, is discontinuous with respect to the Scott topology on L and the product topology on L × L. One example, L₁, is a topology (not, of course, quasi-locally compact) with both meet and join discontinuous. Another, simpler example, L₀, is a sober space in its Scott topology, with join discontinuous (and meet not even separately continuous). I do not know whether L₁ is sober.