Zorn's Lemma - History

History

The Hausdorff maximal principle is an early statement similar to Zorn's lemma.

K. Kuratowski proved in 1922 a version of the lemma close to its modern formulation (it applied to sets ordered by inclusion and closed under unions of well-ordered chains). Essentially the same formulation (weakened by using arbitrary chains, not just well-ordered) was independently given by Max Zorn in 1935, who proposed it as a new axiom of set theory replacing the well-ordering theorem, exhibited some of its applications in algebra, and promised to show its equivalence with the axiom of choice in another paper, which never appeared.

The name "Zorn's lemma" appears to be due to John Tukey, who used it in his book Convergence and Uniformity in Topology in 1940. Bourbaki's Théorie des Ensembles of 1939 refers to a similar maximal principle as "le théorème de Zorn". The name "Kuratowski–Zorn lemma" prevails in Poland and Russia.

Mathematics portal

Read more about this topic:  Zorn's Lemma

Famous quotes containing the word history:

    ... the history of the race, from infancy through its stages of barbarism, heathenism, civilization, and Christianity, is a process of suffering, as the lower principles of humanity are gradually subjected to the higher.
    Catherine E. Beecher (1800–1878)

    It gives me the greatest pleasure to say, as I do from the bottom of my heart, that never in the history of the country, in any crisis and under any conditions, have our Jewish fellow citizens failed to live up to the highest standards of citizenship and patriotism.
    William Howard Taft (1857–1930)

    The one duty we owe to history is to rewrite it.
    Oscar Wilde (1854–1900)