In mathematics, * Lehrbuch der Topologie* (German for "textbook of topology") is a book by Herbert Seifert and William Threlfall, first published in 1934 and published in an English translation in 1980. It was one of the earliest textbooks on algebraic topology, and was the standard reference on this topic for many years.

Albert W. Tucker wrote a review.^{ [1] }

- ↑ Tucker, A. W. (1935). "Review:
*Vorlesungen über die Theorie der Polyeder unter Einschluss der Elemente der Topologie*by Ernest Steinitz, completed by H. Rademacher, and*Lehrbuch der Topologie*by H. Seifert and W. Threlfall" (PDF).*Bulletin of the American Mathematical Society*.**41**(7): 468–471. doi:10.1090/s0002-9904-1935-06116-6.CS1 maint: discouraged parameter (link)

In the part of mathematics referred to as topology, a **surface** is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solids; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space.

**Kazimierz Kuratowski** was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics.

**Armand Borel** was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups.

**Heinz Hopf** was a German mathematician who worked on the fields of topology and geometry.

**Charles Ehresmann** was a German-born French mathematician who worked in differential topology and category theory. He was an early member of the Bourbaki group, and is known for his work on the differential geometry of smooth fiber bundles, notably the Ehresmann connection, the concept of jet bundles, and his seminar on category theory.

**Herbert Karl Johannes Seifert** was a German mathematician known for his work in topology.

In mathematics, particularly in algebraic topology, **Alexander–Spanier cohomology** is a cohomology theory for topological spaces.

**Albert William Tucker** was a Canadian mathematician who made important contributions in topology, game theory, and non-linear programming.

**Hans Julius Zassenhaus** was a German mathematician, known for work in many parts of abstract algebra, and as a pioneer of computer algebra.

A **Seifert fiber space** is a 3-manifold together with a decomposition as a disjoint union of circles. In other words, it is a -bundle over a 2-dimensional orbifold. Many 3-manifolds are Seifert fiber spaces, and they account for all compact oriented manifolds in 6 of the 8 Thurston geometries of the geometrization conjecture.

**Ernst Steinitz** was a German mathematician.

**Béla Kerékjártó** was a Hungarian mathematician who wrote numerous articles on topology.

In mathematics, **real algebraic geometry** is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them.

**Walter Thirring** was an Austrian physicist after whom the Thirring model in quantum field theory is named. He was the son of the physicist Hans Thirring.

The **Faculty of Mathematics and Computer Science** is one of twelve faculties at the University of Heidelberg. It comprises the Institute of Mathematics, the Institute of Applied Mathematics, the School of Applied Sciences, and the Institute of Computer Science. The faculty maintains close relationships to the Interdisciplinary Center for Scientific Computing (IWR) and the Mathematics Center Heidelberg (MATCH). The first chair of mathematics was entrusted to the physician Jacob Curio in the year 1547.

**William Richard Maximilian Hugo Threlfall** was a British-born German mathematician who worked on algebraic topology. He was a coauthor of the standard textbook Lehrbuch der Topologie.

**Willi Ludwig August Rinow** was a German mathematician who specialized in differential geometry and topology. Rinow was the son of a schoolteacher. In 1926, he attended the Humboldt University of Berlin, studying mathematics and physics under professors such as Max Planck, Ludwig Bieberbach, and Heinz Hopf. There, he received his doctorate in 1931. In 1933, he worked at the Jahrbuch über die Fortschritte der Mathematik in Berlin. In 1937, he joined the Nazi Party. During 1937—1940, he was an editor of the journal *Deutsche Mathematik*. In 1937, he became a professor in Berlin and lectured there until 1950. His lecturing was interrupted because of his work as a mathematician at the Oberspreewerk in Berlin from 1946 to 1949.

**Horst Schubert** was a German mathematician.

**Georg Aumann**, was a German mathematician. He was known for his work in general topology and regulated functions. During World War II, he worked as part of a group of five mathematicians, recruited by Wilhelm Fenner, and which included Ernst Witt, Alexander Aigner, Oswald Teichmueller and Johann Friedrich Schultze, and led by Wolfgang Franz, to form the backbone of the new mathematical research department in the late 1930s, which would eventually be called: Section IVc of Cipher Department of the High Command of the Wehrmacht. He also worked as a cryptanalyst, on the initial breaking of the most difficult cyphers. He also researched and developed cryptography theory.

- Herreman, Alain (2005), "Chapter 76. H. Seifert and W. Threlfall (1934) and P. S. Alexandroff and H. Hopf (1935) Books on Topology", in Grattan-Guinness, Ivor (ed.),
*Landmark writings in western mathematics 1640--1940*, Elsevier B. V., Amsterdam, p. 970, ISBN 978-0-444-50871-3, MR 2169816 - Seifert, Herbert; Threlfall, William (1934),
*Lehrbuch der Topologie*,**89**, Leipzig: Teubner, ISBN 9780821835951, MR 0575168 Reprinted by Chelsea Publishing Company 1947 and AMS 2004. - Seifert, Herbert; Threlfall, William (1980), Goldman, Michael A.; Birman, Joan S. (eds.),
*Seifert and Threlfall: a textbook of topology*, Pure and Applied Mathematics,**89**, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], ISBN 978-0-12-634850-7, MR 0575168

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