Zorn's lemma

[[concept]]

Zorn's Lemma

If every chain in a nonempty, partially ordered set $E$ has an upper bound, then $E$ contains a maximal element.

Without Proof

Note

We take this as an axiom of set theory and it can be used to prove the Axiom of Choice
We can also show that every vector space has a Hamel basis

Mentions

File	Last Modified
every vector space has a hamel basis	2025-10-02
Functional Analysis Lecture 4	2025-10-02
Functional Analysis Lecture 5	2025-10-02
Hahn-Banach theorem	2025-10-02
we can always extend functions on subspaces	2025-10-02

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