He studied mathematics, physics, and philosophy as an undergraduate,[2] and began his graduate studies concentrating in algebra and algebraic geometry, but switched to point set topology, the subject of his thesis, despite the general disinterest in the subject in the Netherlands at the time after Brouwer, the Dutch giant in that field, had left it in favor of intuitionism.

He made an important conjecture, only solved much later in 1982 by Pol and 1988 by Kimura,[1] that the compactness degree was the same as the minimum dimension of a set that could be adjoined to the space to compactify it.

This compactness degree, zero, equals the dimension of the single point that may be added to Euclidean space to form its one-point compactification.

A detailed review of de Groot's compactness degree problem and its relation to other definitions of dimension for topological spaces is provided by Koetsier and van Mill[1] In 1959, his work on the classification of homeomorphisms led to the theorem that one can find a large cardinal number, ב2, of pairwise non-homeomorphic connected subsets of the Euclidean plane, such that none of these sets has any nontrivial continuous function mapping it into itself or any other of these sets.

[2][3] From 1962 onwards, his research primarily concerned the development of new topological theories: subcompactness, cocompactness, cotopology, GA-compactification, superextension, minusspaces, antispaces, and squarecompactness.