Hausdorff's Maximal Principle/Formulation 1

Theorem

Let $\struct {\PP, \preceq}$ be a non-empty partially ordered set.

Then there exists a maximal chain in $\PP$.

Also known as

Hausdorff's Maximal Principle is also known as the Hausdorff Maximal Principle.

Some sources call it the Hausdorff Maximality Principle or the Hausdorff Maximality Theorem.

Also see

• Results about Hausdorff's maximal principle can be found here.

Source of Name

This entry was named for Felix Hausdorff.

Sources

• 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 16$: Zorn's Lemma: Exercise $\text{(i)}$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Hausdorff maximality theorem