Properties
In addition, it is known that the following statements are equivalent for any complete lattice L:
- L is completely distributive.
- L can be embedded into a direct product of chains by an order embedding that preserves arbitrary meets and joins.
- Both L and its dual order Lop are continuous posets.
Direct products of, i.e. sets of all functions from some set X to ordered pointwise, are also called cubes.
Read more about this topic: Completely Distributive Lattice
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—John Locke (1632–1704)
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