Johannes de Groot

Johannes de Groot (7 May 1914 – 11 September 1972) was a Dutch mathematician, the leading Dutch topologist for more than two decades following World War II.

Biography De Groot was born at Garrelsweer, a village in the municipality of Loppersum, Groningen, on 7 May 1914. He did both his undergraduate and graduate studies at the Rijksuniversiteit Groningen, where he received his Ph.D. in 1942 under the supervision of Gerrit Schaake. He studied mathematics, physics, and philosophy as an undergraduate, He also visited Purdue University (1959–1960), Washington University in St. Louis (1963–1964), the University of Florida (1966–1967 and winters thereafter), and the University of South Florida (1971–1972). Koetsier and van Mill writes, "His students essentially constitute the topology faculties at the Dutch universities." The deep influence of de Groot on Dutch topology may be seen in the complex academic genealogy of his namesake Johannes Antonius Marie de Groot (shown in the illustration): the later de Groot, a 1990 Ph.D. in topology, is the senior de Groot's academic grandchild, great-grandchild, and great-great-grandchild via four different paths of academic supervision.

De Groot was elected a member of the Royal Netherlands Academy of Arts and Sciences in 1969.

Research De Groot published approximately 90 scientific papers. His mathematical research concerned, in general, topology and topological group theory, although he also made contributions to abstract algebra and mathematical analysis.

He wrote several papers on dimension theory (a topic that had also been of interest to Brouwer). His first work on this subject, in his thesis, concerned the compactness degree of a space: this is a number, defined to be −1 for a compact space, and 1 + x if every point in the space has a neighbourhood the boundary of which has compactness degree x. He made an important conjecture, only solved much later in 1982 by Pol and 1988 by Kimura, A related algebraic result is that every group is the automorphism group of a commutative ring.

Other results in his research include a proof that a metrizable topological space has a non-Archimedean metric (satisfying the strong triangle inequality d(x,z) ≤ max(d(x,y),d(y,z)) if and only if it has dimension zero, description of completely metrizable spaces in terms of cocompactness, and a topological characterization of Hilbert space. From 1962 onwards, his research primarily concerned the development of new topological theories: subcompactness, cocompactness, cotopology, GA-compactification, superextension, minusspaces, antispaces, and squarecompactness.