Friedrich Moritz "Fritz" Hartogs (20 May 1874 – 18 August 1943) was a

German German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ger ...

Jew Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""Th ...

ish mathematician, known for his work on

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

and foundational results on

several complex variables The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions. The name of the field dealing with the properties of function of several complex variables is called several complex variable ...

Life

Hartogs was the son of the merchant Gustav Hartogs and his wife Elise Feist and grew up in

Frankfurt am Main Frankfurt, officially Frankfurt am Main (; Hessian: , "Frank ford on the Main"), is the most populous city in the German state of Hesse. Its 791,000 inhabitants as of 2022 make it the fifth-most populous city in Germany. Located on its na ...

. He studied at the Königliche Technische Hochschule Hannover, at the Technische Hochschule Charlottenburg, at the

University of Berlin Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...

, and at the

Ludwig Maximilian University of Munich The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: Ludwig-Maximilians-Universität München) is a public research university in Munich, Germany. It is Germany's sixth-oldest university in continuous operatio ...

, graduating with a doctorate in 1903 (supervised by

Alfred Pringsheim Alfred Pringsheim (2 September 1850 – 25 June 1941) was a German mathematician and patron of the arts. He was born in Ohlau, Prussian Silesia (now Oława, Poland) and died in Zürich, Switzerland. Family and academic career Pringsheim came ...

). He did his

Habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...

in 1905 and was

Privatdozent ''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualific ...

and Professor in Munich (from 1910 to 1927 extraordinary professor and since 1927 ordinary professor). As a Jew, he suffered greatly under the Nazi regime: he was fired in 1935, was mistreated and briefly interned in

KZ Dachau , , commandant = List of commandants , known for = , location = Upper Bavaria, Southern Germany , built by = Germany , operated by = ''Schutzstaffel'' (SS) , original use = Political prison , construction ...

in 1938, and eventually committed suicide in 1943.

Work

Hartogs main work was in

where he is known for

Hartogs's theorem In mathematics, Hartogs's theorem is a fundamental result of Friedrich Hartogs in the theory of Function of several complex variables, several complex variables. Roughly speaking, it states that a 'separately analytic' function is continuous. Mor ...

, Hartogs's lemma (also known as Hartogs's principle or Hartogs's extension theorem) and the concepts of holomorphic hull and

domain of holomorphy In mathematics, in the theory of functions of Function of several complex variables, several complex variables, a domain of holomorphy is a domain which is maximal in the sense that there exists a holomorphic function on this domain which cannot be ...

. In set theory, he contributed to the theory of wellorders and proved what is also known as

: for every set ''x'' there is a wellordered set that cannot be injectively embedded in ''x''. The smallest such set is known as the

Hartogs number In mathematics, specifically in axiomatic set theory, a Hartogs number is an ordinal number associated with a set. In particular, if ''X'' is any set, then the Hartogs number of ''X'' is the least ordinal α such that there is no injection from α ...

or Hartogs Aleph of ''x''.

References

*. *. Available at th
DigiZeitschriften
*. Available at th
DigiZeitschriften
*

External links

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{{DEFAULTSORT:Hartogs, Friedrich 1874 births 1943 suicides 19th-century German mathematicians 20th-century German mathematicians Scientists from Brussels Complex analysts Mathematical analysts German Jews who died in the Holocaust Suicides by Jews during the Holocaust Academic staff of the Ludwig Maximilian University of Munich