Editing Complete lattice (section)

=== Complete sublattices ===
A sublattice ''M'' of a complete lattice ''L'' is called a ''complete sublattice'' of ''L'' if for every subset ''A'' of ''M'' the elements <math>\bigwedge A</math> and <math>\bigvee A</math>, as defined in ''L'', are actually in ''M''.<ref>Burris, Stanley N., and H.P. Sankappanavar, H. P., 1981. ''[http://www.thoralf.uwaterloo.ca/htdocs/ualg.html A Course in Universal Algebra.]''  Springer-Verlag. {{isbn|3-540-90578-2}} (A monograph available free online).</ref>

If the above requirement is lessened to require only non-empty meet and joins to be in ''M'', the sublattice ''M'' is called a ''closed sublattice'' of ''L''.