Order, lattices, ordered algebraic structures Complete lattices and completions Concept
Dedekind–MacNeille completion
Summary
The Dedekind–MacNeille completion of a partially ordered set is the smallest complete lattice that contains it as an ordered subset. It is built from cuts, pairs of sets of lower and upper bounds. The real numbers are built in the same way from Dedekind cuts of the rationals. Every existing supremum and infimum of the original poset is kept in the completion.
Further reading
About this page
| Tag | DKH4933HMQ |
|---|---|
| URI | m2://DKH4933HMQ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06B23, 06A06 |
| Same as |
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