complete lattice in nLab
Context
-Category theory
Contents
Definition
Definition
A complete lattice is a poset which has all small joins and meets (as opposed to just finite joins and meets).
In particular, it is a lattice.
Complete lattices and complete lattice homomorphisms form a concrete category CompLat.
Examples
- Any power set;
- Any finite inhabited toset;
- The ordered set of real numbers, if a top element and a bottom element are added;
- The unit interval .
Complete lattices are harder to come by in constructive mathematics and nearly impossible in predicative mathematics (at least if they are to be small). In particular, one must use the Mac Neille reals (and be a bit careful about infinity) for the analytic examples to work constructively.
Last revised on March 15, 2012 at 15:39:49. See the history of this page for a list of all contributions to it.