Category:Examples of Complete Lattices
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This category contains examples of Complete Lattice.
Definition 1
Let $\struct {S, \preceq}$ be a lattice.
Then $\struct {S, \preceq}$ is a complete lattice if and only if:
Definition 2
Let $\struct {S, \preceq}$ be an ordered set.
Then $\struct {S, \preceq}$ is a complete lattice if and only if:
- $\forall S' \subseteq S: \inf S', \sup S' \in S$
That is, if and only if all subsets of $S$ have both a supremum and an infimum.
Subcategories
This category has the following 2 subcategories, out of 2 total.
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Pages in category "Examples of Complete Lattices"
The following 6 pages are in this category, out of 6 total.
S
- Set of Closed Elements wrt Closure Operator under Subset Operation is Complete Lattice
- Set of Congruence Classes on Algebraic Structure forms Complete Lattice
- Set of Subgroups forms Complete Lattice
- Set of Submagmas of Magma under Subset Relation forms Complete Lattice
- Set of Subsemigroups forms Complete Lattice