Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Distributive lattice
open-in-new
<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a distributive lattice is a <a href="/facts/Lattice_(order)/5ak6ufky">lattice</a> in which the operations of <a href="/facts/Join_and_meet/cYcLhRIR">join and meet</a> <a href="/facts/Distributivity/0LNBrVJl">distribute</a> over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set <a href="/facts/Union_(set_theory)/KVVXKfWl">union</a> and <a href="/facts/Intersection_(set_theory)/RPfUNJh9">intersection</a>. Indeed, these lattices of sets describe the scenery completely: every distributive lattice is—up to <a href="/facts/Order_isomorphism/PwpVTjW5">isomorphism</a>—given as such a lattice of sets. </p>