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

German German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also Ge ...

Jew Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, religion, and community are highly inte ...

ish mathematician, known for his work on

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), 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 mathema ...

and foundational results on

several complex variables The theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space \mathbb C^n, that is, -tuples of complex numbers. The name of the field dealing with the properties ...

Life

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

Frankfurt am Main Frankfurt am Main () is the most populous city in the States of Germany, German state of Hesse. Its 773,068 inhabitants as of 2022 make it the List of cities in Germany by population, fifth-most populous city in Germany. Located in the forela ...

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

University of Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humbol ...

, and at the

Ludwig Maximilian University of Munich The Ludwig Maximilian University of Munich (simply University of Munich, LMU or LMU Munich; ) is a public university, public research university in Munich, Bavaria, Germany. Originally established as the University of Ingolstadt in 1472 by Duke ...

, 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 the father-in-law of the author and Nobel Prize winner Thomas Mann. Family and academic career Pringsheim was born in Ohlau, Prov ...

). He did his

Habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

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 qualifi ...

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

Dachau concentration camp Dachau (, ; , ; ) was one of the first concentration camps built by Nazi Germany and the longest-running one, opening on 22 March 1933. The camp was initially intended to intern Hitler's political opponents, which consisted of communists, s ...

in 1938, and eventually committed suicide in 1943.

Work

Hartogs' main work was in

where he is known for Hartogs's theorem,

Hartogs's lemma In the theory of functions of Function of several complex variables, several complex variables, Hartogs's extension theorem is a statement about the Singularity (mathematics), singularities of holomorphic functions of several variables. Informall ...

(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 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 extended to a bigger domain. Forma ...

. In set theory, he contributed to the theory of

well-order In mathematics, a well-order (or well-ordering or well-order relation) on a set is a total ordering on with the property that every non-empty subset of has a least element in this ordering. The set together with the ordering is then calle ...

s and proved what is also known as Hartogs's theorem: for every set ''x'' there is a well-ordered 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 � ...

or Hartogs Aleph of ''x''.

References

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

External links

*

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