Teaching at a secondary school was de Groot's first job. Then in 1946 he was appointed as a scientific officer at the Mathematical Centre in Amsterdam. There were two universities in Amsterdam, the University of Amsterdam (founded 1632) and the Free (Vrije) University (founded 1880). The Mathematical Centre, however, was an independent institution not attached to either of these universities.
The following year, de Groot was appointed a lecturer in mathematics at the University of Amsterdam. Then in 1948 he was appointed professor of mathematics at the Technological University of Delft. Four years later, in 1952, he was appointed Professor of Mathematics at the University of Amsterdam. He retained his position at the Mathematical Centre in Amsterdam and, in 1960, was appointed Head of Pure Mathematics there.
In 1964 he became Dean of the Faculty of Science at the University of Amsterdam and, at this time, he gave up his position of Head of Pure Mathematics at the Mathematical Centre but remained associated with the Mathematical Centre as Advisor to Pure Mathematics :-
... actively participating in and in many instances decisively influencing its research activity.De Groot worked in topology and group theory. In group theory one of the topics he studied was that of groups with only trivial automorphisms.
Later de Groot worked on set-theoretic topology. He introduced the concept of co-compactness and other topological concepts.
A recent book, J M Aarts and T Nishiura, Dimension and extensions (1993), has been published discussing a long-standing problem of de Groot. The main conjecture made by him has recently been solved. In a description of the contents of this book the problem of de Groot is described as follows:-
The problem of de Groot concerned compactifications of spaces by means of an adjunction of a set of minimal dimension. This minimal dimension was called the compactness deficiency of a space. Early success in 1942 lead de Groot to invent a generalization of the dimension function, called the compactness degree of a space, with the hope that this function would internally characterize the compactness deficiency which is a topological invariant of a space that is externally defined by means of compact extensions of a space. From this, the two extension problems were spawned.De Groot received many honours, perhaps the most prestigious of which was his election in 1969 to the Royal Dutch Academy of Sciences.
Article by: J J O'Connor and E F Robertson
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