Kuratowski-Zorn lemma

Lemma

Suppose $S$ is any nonempty partially ordered set, where every chain in $S$ has an upper bound in $S$, then $S$ has at least one maximal element

Notes

• statement is equivalent to axiom of choice

See also

• Hahn-Banach theorem

References

1. https://mathworld.wolfram.com/ZornsLemma.html
2. https://ncatlab.org/nlab/show/Zorn's+lemma
3. https://www.bananaspace.org/wiki/Zorn_引理
4. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. New York, NY: Springer New York, 2011, p. 2. doi: 10.1007/978-0-387-70914-7.