Geodesic
Remarks on the sobriety of Scott topology and weak topology on posets
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 531-535.

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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].
Classification : 06B30, 06B35, 54F05
Keywords: sober topological space; Scott topology; weak topology 
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Wei, He; Shouli, Jiang. Remarks on the sobriety of Scott topology and weak topology on posets. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 531-535. http://geodesic.mathdoc.fr/item/CMUC_2002__43_3_a13/