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Remarks on the sobriety of Scott topology and weak topology on posets

He Wei; Jiang Shouli — 2002

Commentationes Mathematicae Universitatis Carolinae

We give some necessary and sufficient conditions for the Scott topology on a complete lattice to be sober, and a sufficient condition for the weak topology on a poset to be sober. These generalize the corresponding results in [1], [2] and [4].

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