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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“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
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—André Breton (1896–1966)
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—G.C. (Georg Christoph)