Leopold Vietoris | |
---|---|

Born | |

Died | (aged 110 years, 309 days) | 9 April 2002

Nationality | Austrian |

Alma mater | TU Wien University of Vienna |

Known for | Contributions to topology Being a supercentenarian |

Spouse(s) | Klara Riccabona (m. 1928–1935) (her death) Maria Josefa Vincentia Vietoris, born von Riccabona zu Reichenfels (m. 1936–2002) (her death) |

Children | 6 |

Scientific career | |

Fields | Mathematics |

Institutions | University of Innsbruck |

Doctoral advisors | Gustav Ritter von Escherich Wilhelm Wirtinger |

**Leopold Vietoris** ( /viːˈtɔːrɪs/ ; German: [viːˈtoːʀɪs] ; 4 June 1891 – 9 April 2002) was an Austrian mathematician, World War I veteran and supercentenarian. He was born in Radkersburg and died in Innsbruck.

He was known for his contributions to topology—notably the Mayer–Vietoris sequence—and other fields of mathematics, his interest in mathematical history and for being a keen alpinist.

Vietoris studied mathematics and geometry at the Vienna University of Technology.^{ [1] } He was drafted in 1914 in World War I and was wounded in September that same year.^{ [1] } On 4 November 1918, one week before the Armistice of Villa Giusti, he became an Italian prisoner of war.^{ [1] } After returning to Austria, he attended the University of Vienna, where he earned his Ph.D. in 1920, with a thesis written under the supervision of Gustav von Escherich and Wilhelm Wirtinger.^{ [1] }^{ [2] }

In autumn 1928 he married his first wife Klara Riccabona, who later died while giving birth to their sixth daughter.^{ [1] } In 1936 he married Klara's sister, Maria Riccabona.^{ [1] }

Vietoris was survived by his six daughters, 17 grandchildren, and 30 great-grandchildren.^{ [3] }

He lends his name to a few mathematical concepts:

**Vietoris topology**(see topological space)**Vietoris homology**(see homology theory)**Mayer–Vietoris sequence****Vietoris–Begle mapping theorem****Vietoris–Rips complex**

Vietoris remained scientifically active in his later years, even writing one paper on trigonometric sums at the age of 103.^{ [4] }

Vietoris lived to be 110 years and 309 days old, and became the oldest verified Austrian man ever.^{ [5] }

- Austrian Decoration for Science and Art (1973)
- Grand Gold Decoration for Services to the Republic of Austria (1981)
- Honorary member of the German Mathematical Society (1992)

- 1 2 3 4 5 6 Reitberger, Heinrich (November 2002). "Leopold Vietoris (1891–2002)" (PDF). American Mathematical Society . Retrieved 5 September 2003.
- ↑ Leopold Vietoris at the Mathematics Genealogy Project
- ↑ "Professor Dr. Leopold Vietoris" (PDF). Geo Imagining. Retrieved 11 October 2009.
- ↑ Reitberger, Heinrich (November 2002). "Leopold Vietoris (1891–2002)" (PDF).
*Notices of the American Mathematical Society*.**49**(10): 1235. - ↑ "Verified Supercentenarians (Ranked By Age) Gerontology Research Group". 1 January 2014. Retrieved 28 February 2019.

In mathematics, a **topological space** is, roughly speaking, a geometrical space in which *closeness* is defined but, generally, cannot be measured by a numeric distance. More specifically, a topological space is a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.

**Algebraic topology** is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.

The **University of Vienna** is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich history, the University of Vienna has developed into one of the largest universities in Europe, and also one of the most renowned, especially in the Humanities. It is associated with 21 Nobel prize winners and has been the academic home to many scholars of historical as well as of academic importance.

**Vietoris** is a surname. Notable people with the surname include:

In mathematics, **homology** is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, to other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topology. Similar constructions are available in a wide variety of other contexts, such as abstract algebra, groups, Lie algebras, Galois theory, and algebraic geometry.

**Samuel Eilenberg** was a Polish-American mathematician who co-founded category theory and Homological Algebra.

In mathematics, **combinatorial topology** was an older name for algebraic topology, dating from the time when topological invariants of spaces were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes. After the proof of the simplicial approximation theorem this approach provided rigour.

In mathematics, particularly algebraic topology and homology theory, the **Mayer–Vietoris sequence** is an algebraic tool to help compute algebraic invariants of topological spaces, known as their homology and cohomology groups. The result is due to two Austrian mathematicians, Walther Mayer and Leopold Vietoris. The method consists of splitting a space into subspaces, for which the homology or cohomology groups may be easier to compute. The sequence relates the (co)homology groups of the space to the (co)homology groups of the subspaces. It is a natural long exact sequence, whose entries are the (co)homology groups of the whole space, the direct sum of the (co)homology groups of the subspaces, and the (co)homology groups of the intersection of the subspaces.

**Sergei Petrovich Novikov** is a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory. In 1970, he won the Fields Medal.

**Heinrich Franz Friedrich Tietze** was an Austrian mathematician, famous for the Tietze extension theorem on functions from topological spaces to the real numbers. He also developed the Tietze transformations for group presentations, and was the first to pose the group isomorphism problem. Tietze's graph is also named after him; it describes the boundaries of a subdivision of the Möbius strip into six mutually-adjacent regions, found by Tietze as part of an extension of the four color theorem to non-orientable surfaces.

**Ernst von Glasersfeld** was a philosopher, and emeritus professor of psychology at the University of Georgia, research associate at the Scientific Reasoning Research Institute, and adjunct professor in the Department of Psychology at the University of Massachusetts Amherst. He was a member of the board of trustees of the American Society for Cybernetics, from which he received the McCulloch Memorial Award in 1991. He was a member of the scientific board of the Instituto Piaget, Lisbon.

The **Vietoris–Begle mapping theorem** is a result in the mathematical field of algebraic topology. It is named for Leopold Vietoris and Edward G. Begle. The statement of the theorem, below, is as formulated by Stephen Smale.

In mathematics, specifically in algebraic topology, the **Eilenberg–Steenrod axioms** are properties that homology theories of topological spaces have in common. The quintessential example of a homology theory satisfying the axioms is singular homology, developed by Samuel Eilenberg and Norman Steenrod.

**Walther Mayer** was an Austrian mathematician, born in Graz, Austria-Hungary. With Leopold Vietoris he is the namesake of the Mayer–Vietoris sequence in topology. He served as an assistant to Albert Einstein, and was nicknamed "Einstein's calculator".

**Prince Friedrich of Saxe-Meiningen, Duke of Saxony** was a German soldier and member of the Ducal House of Saxe-Meiningen.

**Herman Francis Mark** was an Austrian-American chemist regarded for his contributions to the development of polymer science. Mark's x-ray diffraction work on the molecular structure of fibers provided important evidence for the macromolecular theory of polymer structure. Together with Houwink he formulated an equation, now called the Mark–Houwink or Mark–Houwink–Sakurada equation, describing the dependence of the intrinsic viscosity of a polymer on its relative molecular mass. He was a long-time faculty at Polytechnic Institute of Brooklyn. In 1946, he established the *Journal of Polymer Science*.

In topology, the **Vietoris–Rips complex**, also called the **Vietoris complex** or **Rips complex**, is an abstract simplicial complex that can be defined from any metric space *M* and distance δ by forming a simplex for every finite set of points that has diameter at most δ. That is, it is a family of finite subsets of *M*, in which we think of a subset of *k* points as forming a (*k* − 1)-dimensional simplex ; if a finite set *S* has the property that the distance between every pair of points in *S* is at most δ, then we include *S* as a simplex in the complex.

**Nikolaus Hofreiter** was an Austrian mathematician who worked mainly in number theory.

**Robert Hammerstiel** was an Austrian painter and engraver. His works are influenced by Serbian icon painting, wood-cut engraving and pop art. Hammerstiel was internationally recognized and received numerous awards. His home town installed a museum dedicated to his art.

**Dan Burghelea** is a Romanian-American mathematician, academic and researcher. He is an Emeritus Professor of Mathematics at Ohio State University.

- Weibel, Peter, ed. (2005).
*Beyond Art: A Third Culture: A Comparative Study in Cultures, Art and Science in 20th Century Austria and Hungary*. Springer Science & Business Media. p. 260. ISBN 978-3-211-24562-0.

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