Eugen Otto Erwin Netto (30 June 1848 – 13 May 1919) 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 ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. He was born in

Halle Halle may refer to: Places Germany * Halle (Saale), also called Halle an der Saale, a city in Saxony-Anhalt ** Halle (region), a former administrative region in Saxony-Anhalt ** Bezirk Halle, a former administrative division of East Germany ** Hall ...

and died in

Giessen Giessen, spelled Gießen in German (), is a town in the German state (''Bundesland'') of Hesse, capital of both the district of Giessen and the administrative region of Giessen. The population is approximately 90,000, with roughly 37,000 univer ...

. Netto's theorem, on the dimension-preserving properties of continuous bijections, is named for Netto. Netto published this theorem in 1878, in response to

Georg Cantor Georg Ferdinand Ludwig Philipp Cantor ( , ; – January 6, 1918) was a German mathematician. He played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of ...

's proof of the existence of discontinuous bijections between the

unit interval In mathematics, the unit interval is the closed interval , that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1. It is often denoted ' (capital letter ). In addition to its role in real analys ...

and

unit square In mathematics, a unit square is a square whose sides have length . Often, ''the'' unit square refers specifically to the square in the Cartesian plane with corners at the four points ), , , and . Cartesian coordinates In a Cartesian coordina ...

. His proof was not fully rigorous, but its errors were later repaired.

Works

''Substitutionentheorie und ihre Anwendung auf die Algebra.''
Teubner 1882.
''Theory of Substitutions and Its Applications to Algebra.''
Ann Arbor, Mich. 1892.
''Die Determinanten.''
Teubner, 1910. *''Die Determinanten.'' Teubner, 2nd edition 1925.
''Lehrbuch der Combinatorik.''
Teubner, 1901, 2nd edition 1927.
''Elementare Algebra.''
Teubner 1904.
''Gruppen- und Substitutionentheorie.''
Leipzig, Göschen, 1908.
''Vorlesungen über Algebra. Erster Band.''
Teubner, 1896.
''Vorlesungen über Algebra. Zweiter Band.''
Teubner, 1900. *Netto
''Kombinatorik.''
Enzyklopädie der Mathematischen Wissenschaften, Bd.1, 1898. *Netto
''Rationale Funktionen einer Veränderlichen; ihre Nullstellen.''
Enzyklopädie Math.Wiss., Bd.1, 1899. *Netto
''Rationale Funktionen mehrerer Veränderlichen.''
Enzyklopädie Mathem.Wiss., Bd.1, 1899.

References

1848 births 1919 deaths 19th-century German mathematicians People from Halle (Saale) People from the Province of Saxony 20th-century German mathematicians {{germany-mathematician-stub