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 Oswald Wyler
Professor Emeritus
Dr.sc.math., Swiss Federal Institute of Technology, Zürich
E-mail: owyler@andrew.cmu.edu
Research
My research concerns the theory of categories, and in particular the applications of categories to general topology, logic and continuous lattices. For category theory, a set theory is a particular type of category, called a topos. Topoi give a convenient access to non-standard and intuitionistic set theory; they are also important for algebraic geometry.
For general topology, a generalization of topoi called quasitopoi, has become increasingly important. In a quasitopos, many set-theoretic constructions can be carried out that are not possible in ordinary topology, but the topology is still not entirely lost. Quasitopoi have also become increasingly important in the theory of fuzzy sets and systems.
Selected Publications
Wyler, O. Lecture Notes on Topoi and Quasitopoi, World Scientific, Singapore, 1991.
Wyler, O. "Quotient-topological Completions and Hulls of Concrete Categories," TR 91–136, Department of Mathematics, Carnegie Mellon University.
Wyler, O. (1989), "On Convergence of Filters and Ultrafilters to Subsets," Lecture Notes in Computer Science 393: 340–350.
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