Dedekind–MacNeille completion of a partially ordered set is the smallest complete lattice that contains it. It is named after Holbrook Mann MacNeille...

the Dedekind–MacNeille completion of S consists of all subsets A for which (Au)l = A; it is ordered by inclusion. The Dedekind-MacNeille completion is...

Completion (metric space), constructing the smallest complete metric space containing a given space Construction of a complete measure space Dedekind–MacNeille...

some subset of A. As a partially ordered set, this completion of A is the Dedekind–MacNeille completion. More generally, if κ is a cardinal then a Boolean...

Dedekind–Hasse norm Dedekind-infinite set Dedekind–MacNeille completion Dedekind's axiom Dedekind's complementary module Dedekind lattice Jordan–Dedekind lattice...

free lattices, Grothendieck group, completion of a metric space, completion of a ring, Dedekind–MacNeille completion, product topologies, Stone–Čech compactification...

achieved through the so-called Dedekind–MacNeille completion. For this process, elements of the poset are mapped to (Dedekind-) cuts, which can then be mapped...

\mathbb {R} \cup \left\{-\infty ,+\infty \right\}.} It is the Dedekind–MacNeille completion of the real numbers. When the meaning is clear from context...

can work on the dual order explicitly. By analogy with the Dedekind–MacNeille completion of a partially ordered set, every partially ordered set can...

meets. Completion. A completion of a poset is an order-embedding of the poset in a complete lattice. Completion by cuts. Synonym of Dedekind–MacNeille completion...