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| Title of object: |
complete lattice |
| Canonical Name: |
CompleteLattice |
| Type: |
Definition |
| Created on: |
2002-08-17 23:15:37 |
| Modified on: |
2007-01-28 11:28:04 |
| Classification: |
msc:06B23, msc:03G10 |
| Defines: |
countably complete lattice, countably-complete lattice |
Preamble:
Content:
A \emph{complete lattice} is a poset $P$
such that every subset of $P$ has both a supremum and an infimum in $P$.
A \emph{countably complete lattice} is a poset $P$
such that every countable subset of $P$ has both a supremum and an infimum in $P$.
Note that every complete lattice is a countably complete lattice,
and every countably complete lattice is a bounded lattice.
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