Prof Guillaume Brümmer

Emeritus Professor of Mathematics

Degrees: M.Sc. (Stell.); Doctorandus Math. (Amsterdam); Ph.D. (Cape Town)
Email: gcl.brummer@uct.ac.za

Honours:

  • FRD A-rating
  • Fellow of the University of Cape Town (1989);
  • Havenga Prize of the Suid-Afrikaanse Akademie vir Wetenskap en Kuns (1991);
  • Award of the South African Mathematical Society for Distinction in Research (1994) 

Teaching and research interests:

Our work ranges through several branches of topology and category theory. Although these two fields of mathematics have multitudes of applications inside and outside of mathematics, they have a certain reputation for being rather more abstract than many other fields of mathematics. It is then sharply questioned whether studies of such abstraction are beneficial to the technological and economical development of South Africa. My view is that these studies are essential not only because of their proven applications but also because they form the foundation for the understanding of major parts of the subject. Moreover, the blend of topology with category theory offers a special bonus. Category theory is that branch of mathematics which provides paradigms or structural models for many apparently dissimilar mathematical phenomena, thereby providing a unifying, systematic perspective and economy of effort. As methodology, it can guide the researcher toward meaningful topics and fruitful links with applicable work.

Representative publications:

  1. (with B. Banaschewski) Stably continuous frames, Math. Proc. Cambr. Philos. Soc. 104 (1988), 7-19.
  2. (with B. Banaschewski) Strong zero-dimensionality of biframes and bispaces, Quaestiones Mathematicae 13 (1990), 273-290.
  3. (with E. Giuli and H. Herrlich) Epireflections which are completions, Cahiers Topol. Géom. Diff. Cat. 33 (1992), 71-93.
  4. (with E. Giuli) A categorical concept of completion of objects, Comment. Math. Univ. Carolinae 33 (1992), 131-147.
  5. Completions of functorial topological structures, in `Recent Developments of General Topology and its Applications' (ed) W. Gähler et al., Akademie-Verlag, Berlin, 1992, pp60-71
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