Egbert Harzheim

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Egbert Harzheim (2004)

Egbert Harzheim (born February 11, 1932 in Cologne ; † December 14, 2012 ) was a German mathematician who worked on pure mathematics , including set theory , order theory , topology and discrete mathematics .

Scientific career and achievements

Egbert Harzheim studied mathematics at the University of Cologne from 1952 to 1957 and passed the state examination there in 1958 , where he obtained his doctorate in 1961 (under the supervision of Klaus Wagner and Karl Dörge ) and finally his habilitation in 1965 . From 1965 to 1970 he was a lecturer , first at the University of Cologne from 1965 to 1968, and later from 1968 to 1970 at the University of Düsseldorf . He spent the 1970/71 winter semester as a visiting professor at the Technical University of Berlin . From 1970 until his death in 2012, Egbert Harzheim taught at the Mathematical Institute of the University of Düsseldorf , initially until 1997 as a scientific advisor and professor and then as Prof. i. R. He supervised five doctoral students : Hans-Josef Scholz (1987), Christoph Josten (1987), Manfred Fechner (1989), Christoph-Ulrich Schulte (1992) and Klaus Dohmen (1993).

Last but not least, Egbert Harzheim achieved significant results in order theory . His name is particularly associated with a theorem about the order dimension of certain partially ordered sets , known as the Harzheim Theorem .

Author activity

Egbert Harzheim was the author or co-author of around 38 scientific publications :

Mathematical textbooks

  • Egbert Harzheim, Helmut Ratschek: Introduction to General Topology (=  THE MATHEMATICS. Introductions to the subject matter and results of its sub-areas and related sciences ). Scientific Book Society , Darmstadt 1978, ISBN 3-534-06355-4 . MR0380697
  • Egbert Harzheim: Introduction to combinatorial topology (=  mathematics. Introductions to the subject matter and results of its sub-areas and related sciences ). Scientific Book Society, Darmstadt 1978, ISBN 3-534-07016-X ( MR0533264 ).
  • Egbert Harzheim: Ordered Sets (=  Advances in Mathematics . Volume 7 ). Springer Verlag , New York, NY 2005, ISBN 0-387-24219-8 . MR2127991

Original scientific papers (selection)

  • Egbert Harzheim: Contributions to the theory of order types, in particular the η α -sets . In: Math. Ann . tape 154 , 1964, pp. 116-134 . MR0161807
  • Egbert Harzheim: About the basics of universal algebra . In: Math . tape 31 , 1966, pp. 39-52 . MR0191857
  • Egbert Harzheim: Combinatorial considerations on the structure of the power set . In: Math . tape 34 , 1967, p. 123-141 . MR0216960
  • Egbert Harzheim: A combinatorial problem about selection functions . In: Publ. Math. Debrecen . tape 15 , 1968, p. 19-22 . MR0244060
  • Egbert Harzheim: Block systems on a lot (In: Theory of sets and topology (in honor of Felix Hausdorff, 1868-1942). Ed. Günter Asser) . Deutscher Verlag der Wissenschaften , Berlin 1972, p. 221-232 . MR0347612
  • Egbert Harzheim: A combinatorial theorem related to the Jordan-Brouwer separation theorem (In: Infinite and finite sets. Vol. II. Edited by András Hajnal , Richard Rado , Vera T. Sós ) (=  Colloquia mathematica Societatis János Bolyai . Volume 10 ). North-Holland Publishing Company , Amsterdam [ua] 1975, ISBN 0-7204-2814-9 , pp. 853-855 .
  • Egbert Harzheim: Decomposition theorems for weakened injective mappings . In: Math. Ann . tape 252 , 1980, pp. 247-257 . MR0593637
  • Egbert Harzheim: A constructive proof for a theorem on contractive mappings in power sets . In: Discrete Mathematics . tape 45 , 1983, pp. 99-106 . MR0700853
  • Frank Harary and Egbert Harzheim: The degree sets of connected infinite graphs . In: Fund. Math . tape 118 , 1983, pp. 233-236 . MR0736283
  • Egbert Harzheim: On topological properties of cartesian products of linearly ordered continua (In: Orders: Description and Roles (Proceedings of the Conference on Ordered Sets and their Applications, Château de la Tourette, l'Arbresle, July 5-11, 1982). Edited by Maurice Pouzet and Denis Richard) (=  North-Holland Mathematical Studies . Volume 99 ). Elsevier Science Publishers, Amsterdam [et al.] 1984, ISBN 0-444-87601-4 , pp. 171-192 . MR0779852
  • Egbert Harzheim: Generalization of the decomposition theorem by Jordan-Brouwer-Alexander to products of linearly ordered continuities . In: Arch. Math . tape 46 , 1986, pp. 271-274 . MR0834848
  • Paul Erdős and Egbert Harzheim: Congruent subsets of infinite sets of natural numbers . In: J. Reine Angew. Math . tape 367 , 1986, pp. 207-214 . MR0839132

Individual evidence

  1. ↑ A largely comprehensive overview can be found here .
personal data
SURNAME Harzheim, Egbert
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH February 11, 1932
PLACE OF BIRTH Cologne
DATE OF DEATH December 14, 2012