Linked from

The 12 pages that link to Zorn's lemma, each with the reason it gives.

• Well-ordering theoremRelated: It is equivalent to the well-ordering theorem in standard set theory.

• Maximal idealRelated: Its application to proper ideals proves the maximal ideal theorem.

• Algebraic closureRelated: It supports existence proofs for maximal algebraic extensions, from which algebraic closures can be obtained.

• Choice functionRelated: It is equivalent to the axiom of choice and often proves existence without constructing selections.

• Tychonoff's theoremRelated: It is a common choice principle used in proofs of product compactness.

• UltrafilterRelated: It proves that a proper filter can be extended to an ultrafilter.

• Chain (order theory)Related: Its hypothesis is stated for all chains, including infinite ones.

• Boolean prime ideal theoremRelated: Zorn's lemma proves the theorem, though it assumes the stronger axiom of choice.

• Kirszbraun theoremRelated: Maximal partial extensions turn the one-point construction into a full-domain extension.

• Krein–Milman theoremRelated: A maximal-face argument can use Zorn's lemma to obtain a minimal nonempty compact face.

• Krull's theoremRelated: Applied to proper ideals, it supplies the maximal element the theorem asserts exists.