# 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.