Maximal Principles are Equivalent

Theorem
The Maximal Principles are equivalent:


 * Kuratowski's Lemma


 * Tukey's Lemma


 * Zorn's Lemma


 * Hausdorff's Maximal Principle

Proof
We have:


 * Kuratowski's Lemma implies Tukey's Lemma


 * Tukey's Lemma implies Zorn's Lemma


 * Zorn's Lemma implies Hausdorff's Maximal Principle


 * Hausdorff's Maximal Principle implies Kuratowski's Lemma