On 7/7/2010 5:31 AM, Paul Taylor wrote:
Non-Hausdorff topologies, in particular the Scott topology, have been one of the most important features of mathematics applied to computer science over the past forty years.
Surely it is now time for this material to be included in the standard undergraduate curriculum for general topology in pure mathematics degree programmes.
Dear Paul et al: I certainly learned about non-Hausdorff topologies in the topology course I took as an undergraduate from Michael Edelstein at Dalhousie (using Kelley's "General Topology" as a text). The Zariski topology also appeared in a couple courses, and various instructors recommended the book "Counterexamples in Topology" by Steen and Seebach, which gives a fairly good "tour of the zoo". Nonetheless, thirty year later, I would certainly accept that a modern treatment of the topic would have a somewhat different focus, for precisely the reasons that you give in your first paragraph. -Robert [For admin and other information see: http://www.mta.ca/~cat-dist/ ]