Re: non-Hausdoff topology

[Steve Vickers <s.j.vickers@cs.bham.ac.uk>]

Dear Paul,

At the Open University I was in the course development team for a
thorough revision of the Topology course. Some of the other members
started with the opinion that there was no need to go beyond metric
spaces. However, it did eventually include general topology, mostly
Hausdorff, and material on surfaces and their classification.

I wrote a 50 page unit on "Topology and Computation" for it, including
the specialization order, some finite topological spaces (at one point I
had a section giving the equivalence between them and preorders),
function spaces in some simple domain settings, continuity of currying
and uncurrying and recursion as limit points. However, I left before the
course development was finished, and the others didn't feel brave enough
to include such wacky material without me there.

So I thought in 2001 that it was time for this material to be included
in the standard undergraduate curriculum for general topology, but
failed to convince the people who might actually include it.

Regards,

Steve.

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.
>
> I wonder whether "categories" reader have some comments on their
> experience of trying to do this?   I am thinking of the possible
> reactions from both students and colleagues.
>
> Paul Taylor
>


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