Examples
Unlike complete posets, chain complete posets are relatively common. Examples include:
- Any complete poset
- The set of all linearly independent subsets of a vector space V, ordered by inclusion.
- The set of all partial functions on a set, ordered by restriction.
- The set of all partial choice functions on a collection of non-empty sets, ordered by restriction.
- The set of all prime ideals of a ring, ordered by inclusion.
- The set of all consistent theories of a first-order language.
Read more about this topic: Chain Complete
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“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
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—Bernard Mandeville (1670–1733)