Editing Felix Hausdorff (section)

===First professorship===
In December 1901 Hausdorff was appointed as adjunct associate professor at the University of Leipzig. An often-repeated [[factoid]], that Hausdorff got a call from [[Göttingen]] and rejected it, cannot be verified and is most likely wrong. After considering Hausdorff's application to Leipzig, the Dean Kirchner felt compelled to make the following addition to the very positive vote from his colleagues, written by Heinrich Bruns:

{{blockquote|The faculty, however, considers itself obliged to report to the Royal Ministry that the above application, considered on November 2nd of this year when a faculty meeting had taken place, was not accepted by all, but with 22 votes to 7. The minority was opposed, because Dr. Hausdorff is of the Mosaic faith.<ref>Archiv der Universität Leipzig, PA 547</ref>}}

This quote emphasizes the undisguised [[anti-Semitism|antisemitism]] present, which especially took a sharp upturn throughout the German Reich after the [[Gründerkrach|stock market crash of 1873]]. Leipzig was a focus of antisemitic sentiment, especially among the student body, which may well be the reason that Hausdorff did not feel at ease in Leipzig. Another contributing factor may also have been the stresses due to the hierarchical posturing of the Leipzig professors.

After his Habilitation, Hausdorff wrote other works on [[optics]], on [[non-Euclidean geometry]], and on [[hypercomplex number]] systems, as well as two papers on [[probability theory]]. However, his main area of work soon became set theory, especially the theory of [[ordered set]]s. Initially, it was only out of philosophical interest that Hausdorff began to study [[Georg Cantor]]'s work, beginning around 1897, but already in 1901 Hausdorff began lecturing on set theory. His was one of the first ever lectures on set theory; only [[Ernst Zermelo]]'s lectures in Göttingen College during the winter of 1900/1901 were earlier. That same year, he published his first paper on order types in which he examined a generalization of [[well-ordering]]s called [[graded order types]], where a [[linear order]] is graded if no two of its segments share the same [[order type]]. He generalized the [[Cantor–Bernstein theorem]], which said the collection of countable order types has the [[cardinality of the continuum]] and showed that the collection of all graded types of an [[Idempotence|idempotent]] cardinality {{var|m}} has a cardinality of 2<sup>{{var|m}}</sup>.<ref>{{Cite book|title = Handbook of the History of Logic: Sets and extensions in the twentieth century|url = https://books.google.com/books?id=ZF_QckMFy-oC&q=graded%2520order%2520type&pg=PA159|publisher = Elsevier|date = 2012-01-01|isbn = 9780444516213|language = en|first = Dov M.|last = Gabbay}}</ref>

For the summer semester of 1910 Hausdorff was appointed as professor to the [[University of Bonn]]. There he began a lecture series on set theory, which he substantially revised and expanded for the summer semester of 1912.

In the summer of 1912 he also began work on his magnum opus, the book ''Basics of set theory''. It was completed in [[Greifswald]], where Hausdorff had been appointed for the summer semester as full professor in 1913, and was released in April 1914.

The [[University of Greifswald]] was the smallest of the Prussian universities. The mathematical institute there was also small; during the summer of 1916 and the winter of 1916/17, Hausdorff was the only mathematician in Greifswald. This meant that he was almost fully occupied in teaching basic courses. It was thus a substantial improvement for his academic career when Hausdorff was appointed in 1921 to Bonn. There he was free to teach about wider ranges of topics, and often lectured on his latest research. He gave a particularly noteworthy lecture on probability theory (NL Hausdorff: Capsule 21: Fasz 64) in the summer semester of 1923, in which he grounded the theory of probability in measure-theoretic axiomatic theory, ten years before [[Andrey Kolmogorov|A. N. Kolmogorov]]'s "Basic concepts of probability theory" (reprinted in full in the collected works, Volume V). In Bonn, Hausdorff was friends and colleagues with [[Eduard Study]], and later with [[Otto Toeplitz]], who were both
outstanding mathematicians.