- Felix Hausdorff
name = Felix Hausdorff
image_width = 300px
birth_date = Birth date|1868|11|8
death_date = death date and age|1942|1|26|1868|11|8
University of Bonn, University of Greifswald
University of Leipzig
Heinrich Bruns Adolph Mayer
Karl Bögel Franz Hallenbach Gustav Steinbach
Hausdorff measure Hausdorff dimension
Felix Hausdorff (
November 8, 1868– January 26, 1942) was a German mathematicianwho is considered to be one of the founders of modern topologyand who contributed significantly to set theory, descriptive set theory, measure theory, function theory, and functional analysis.
Hausdorff studied at the
University of Leipzig, obtaining his Ph.D. in 1891. He taught mathematics in Leipzig until 1910, when he became professor of mathematics at the University of Bonn. He was professor at the University of Greifswaldfrom 1913 to 1921. He then returned to Bonn. When the Nazis came to power, Hausdorff, who was Jewish, felt that as a respected university professor he would be spared from persecution. However, his abstract mathematics was denounced as "Jewish", useless, and "un-German"Fact|date=July 2007 and he lost his position in 1935. Though he could no longer publish in Germany, Hausdorff continued to be an active research mathematician, publishing in the Polish journal Fundamenta Mathematicae. After Kristallnachtin 1938 as persecution of Jews escalated, Hausdorff became more and more isolated. Finally, in 1942 when he could no longer avoid being sent to a concentration camp, Hausdorff committed suicidetogether with his wife and sister-in-law on the 26th of January.
Hausdorff was the first to state a generalization of Cantor's
Continuum Hypothesis; his Aleph Hypothesis, which appears in his 1908 article Grundzüge einer Theorie der geordneten Mengen, and which is equivalent to what is now called the Generalized Continuum Hypothesis.
In 1909, while studying partially ordered sets of real sequences, he stated what is now known as the Hausdorff Maximal Principle; he was the first to apply a maximal principle in algebra.
In his 1914 classic text,
Grundzüge der Mengenlehre, he defined and studied partially ordered sets abstractly; using the Axiom of Choice, he proved that every partially ordered set has a maximal linearly ordered subset. In this same book, he axiomatized the topological concept of neighborhood and introduced the topological spaces that are now called Hausdorff spaces.
In 1914 using the
Axiom of Choice, he gave a "paradoxical" decomposition of the 2-sphereas the disjoint union of four sets A,B,C, and Q, where Q is countable and the sets A, B, C, and BC are mutually congruent. This later inspired the Banach-Tarski paradoxical decomposition of the ball in 3-space.
He introduced the concepts now called
Hausdorff measureand Hausdorff dimension, which have been useful in the theory of fractals. In analysis, he solved what is now called the Hausdorff moment problem.
Hausdorff also published philosophical and literary works under the pseudonym "Paul Mongré". "Paul Mongre" published a number of books and articles on the philosopher Friedrich Nietzsche, as well as a number of reviews of contemporary literature and drama. Mongre-Hausdorff also published a satirical play which performed in a dozen German cities. In the course of attempts to refute Nietzsche's doctrine of "the eternal return of the same," Hausdorff was led to Cantor's set theory, which set Hausdorff on the road to his set-theoretical discoveries. Hausdorff's Nietzschean philosophical writings appear in volume VII of his collected works.
Grundzüge der Mengenlehre"
* [Gesamnelte Werke]
* [http://www.aic.uni-wuppertal.de/fb7/hausdorff/ Homepage of the Hausdorff Edition (German)]
* [http://www.ulb.uni-bonn.de/bibliothek/veroeffentlichungen&ausstellungen/veroeffentlichungen/hausdorff.pdf Hausdorff Findbuch]
* [http://www.hausdorff-center.uni-bonn.de/ Hausdorff Center for Mathematics in Bonn]
NAME= Hausdorff, Felix
DATE OF BIRTH= birth date|1868|11|8|mf=y
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DATE OF DEATH= death date|1942|1|26|mf=y
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