In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914 (Moore 1982:168). It states that in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.
The Hausdorff maximal principle is one of many statements equivalent to the axiom of choice over Zermelo–Fraenkel set theory. The principle is also called the Hausdorff maximality theorem or the Kuratowski lemma (Kelley 1955:33).
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