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A Lattice Theoretical Form of the Alexander's Subbase Theorem

Xu Xiaoquan (Department of Mathematics,Jiangxi Normal University,Nanchang 330027)  
In this note,we generalize the classical Alexander' subbase theorem in general topology to the case of complete distributive lattices,and give a similar result for the completely below relation.As a by product,we obtain a characterization of complete distributivity.
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