Geodesic
Metrizable completely distributive lattices
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 1, pp. 137-148.

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The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements.
Classification : 06B30, 06B35, 06D10, 54C08, 54C15, 54C55, 54E35, 54H12
Keywords: completely distributive lattice; interval topology; AR; ANR 
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De-Xue, Zhang. Metrizable completely distributive lattices. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 1, pp. 137-148. http://geodesic.mathdoc.fr/item/CMUC_1997__38_1_a11/