Ordered Sets: An Introduction

acyclic algorithm antichain automorphism backtracking called classes of ordered comparability graph comparability invariant complete lattice consider constraint contains contradiction critical pair deck decomposition Dedekind-MacNeille completion define Definition distributive lattice End(P endomorphism example Exercise fence finite ordered set fixed point free fixed point property forward checking free order-preserving map function graded ordered sets hence implies infimum interval ordered set irreducible point isomorphic isotone relation largest element let f lexicographic sum linear extensions lower bounds map f maximal elements maximal order-autonomous subsets Moreover nonempty nontrivial order relation order-preserving self map point free order-preserving point property iff polynomial proof of Theorem Proposition Prove reader reconstructible result retraction sequence set and let set in Figure sets of width simplicial complex singleton smallest element supremum T-dismantlable topological trivial truncated lattice upper bound upper cover Zorn's Lemma