monotonic function infimum and supremum partially ordered set interval (mathematics) lexicographic order total order embedding upper and lower bounds zorn's lemma ordered pair dedekind cut order theory hasse diagram well-order preorder maximal and minimal elements möbius inversion formula filter (mathematics) join and meet ultrafilter antichain weak ordering galois connection directed set inversion (discrete mathematics) trichotomy (mathematics) order topology greatest element and least element infinite divisibility closure operator causal sets majorization supermodular function completeness (order theory) multitree ascending chain condition monomial order well-quasi-ordering cofinality complete partial order alexandrov topology incidence algebra cyclic order linear extension comparability graph cofinal (mathematics) comparability boolean prime ideal theorem 1/3–2/3 conjecture upper set scott continuity order isomorphism stone duality duality (order theory) ultrafilter (set theory) kleene fixed-point theorem dense order hausdorff maximal principle dedekind– mac neille completion suslin's problem greedoid product order graded poset bruhat order schur– horn theorem quantale complete boolean algebra least fixed point order dimension covering relation atom (order theory) shortlex order fréchet filter glossary of order theory betweenness order polynomial prefix order sorting algorithms countable chain condition complete heyting algebra chain-complete partial order cantor– bernstein theorem list of order structures in mathematics order embedding banach lattice topkis's theorem teichmüller– tukey lemma semiorder poset topology
Mathematics_Fields of mathematics