KnowraChain (order theory)Linked fromLinked fromThe 8 pages that link to Chain (order theory), each with the reason it gives.All 8Broader topic 3Related 4Compared with 1Partial orderBroader topic: A chain is the totally ordered portion of a partial order.Partially ordered setBroader topic: Chains isolate the parts of the order that behave like total orders.Zorn's lemmaBroader topic: The hypothesis requires every such totally ordered subset to have an upper bound.AntichainCompared with: Chains require pairwise comparability, the opposite condition to antichains.Maximal elementRelated: Maximal elements terminate certain chains, while Zorn's lemma reasons over all chains.Dilworth's theoremRelated: The theorem’s minimum counts chains in a partition.Krull's theoremRelated: Unions of chains of proper ideals provide the upper bounds required by Zorn's lemma.Teichmüller–Tukey lemmaRelated: Unions of chains preserve finite character, supplying the upper bounds behind maximality arguments.