The construction of functorial quasi-uniformities
by
Hans-Peter A. Kunzi
Dept. Math. Appl. Math., University of Cape Town, Rondebosch 7701, South Africa
Coauthors: G.C.L. Bruemmer (Dept. Math. Appl. Math., University of Cape Town, Rondebosch 7701, South Africa)

We consider functors F:Top₀ --> Quu₀ from the category of topological T₀ spaces to the category of quasi-uniform T₀ spaces which endow the T₀ spaces with compatible quasi-uniformities. Let T:Quu₀ --> Top₀ be the usual forgetful functor and let us regard the bicompletion as a functor K:Quu₀ - > Quu₀.

Bruemmer called a functorial quasi-uniformity F K-true if KF=FTKF holds. Junnila's well-monotone quasi-uniformity W is a typical example of a K-true functorial quasi-uniformity according to a result of Ferrario and Kunzi; indeed they showed more precisely that TKW is the sobrification functor and that the well-monotone quasi-uniformity of the sobrification of a T₀ space X coincides with the bicompletion of the well-monotone quasi-uniformity of X. In his Ph.D. thesis, with the help of a superrigid space due to van Douwen, Kimmie constructed a functorial quasi-uniformity F finer than W such that the functor TKF is idempotent, although F is not K-true.

We shall discuss in our talk how Kimmie's example can be modified to answer some further interesting questions concerning the behaviour of functorial quasi-uniformities under the bicompletion functor K.

http://at.yorku.ca/h/a/a/a/30.htm

Date received: November 19, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafw-03.