Associate Professor in Mathematics

Degrees: M.Sc., Ph.D. (Cape Town)

Email: crag@maths.uct.ac.za

Personal Web Page: None

Teaching and research interests:

My special interest is to treat topologies as certain lattices called frames. In particular I use -frames (generalisations of, for example, cozero-set lattices of topological, uniform or nearness spaces) to study properties of topological spaces such as realcompactness and pseudocompactness and to develop a dimension theory for frames.

Graduate teaching and thesis supervision: Categorical and general topology, rings of continuous functions, frames, sigma-frames and dimension theory.

Undergraduate teaching: I particularly enjoy teaching Real Analysis, Topology (Metric Spaces), Lattices and Order. Since my appointment as Education Development Officer for the Department I have been especially concerned with curriculum development at undergraduate and Honours level.

Representative publications:

Realcompact spaces and regular -frames, Math. Proc. Cambr. Philos. Soc. 96 (1984), 73-79.

(with B. Banaschewski and J.L. Frith) On the congruence lattice of a frame, Pacific J. Math. 130 (1987), 209-213.

(with B. Banaschewski) Stone-Cech compactification and dimension theory for regular sigma-frames, J. Lond. Math. Soc. (2) 39 (1989) no.1, 1-8.

(with B. Banaschewski) Pseudocompactness and the cozeso part of a frame, Comment. Math. Univ. Carolinae 37,3 (1996) 577-587.