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
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