Re: non-Hausdoff topology

[Martin Escardo <m.escardo@cs.bham.ac.uk>]

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.

Ok, here is an experience (about 3 years ago, I think). One day I went
for lunch on my own at the university's Staff House, and I sat at a
table in which the only other person turned out to be an analyst in the
maths department, at retirement age. After I asked about his work, he
asked about mine, and I said I was in computer science, and that parts
of my work involved the use of topology in understanding computation. So
far so good, and I had an attentive and inquisitive listener for
probably more than 1/2 hour, at which point he queried more about the
nature of the spaces one comes up with in this field. The first thing I
answered was that often they were not Hausdorff. And that was also the
last, because he looked in amazement and disbelief, said that then these
were not really topological spaces, checked his watch, said something
incomprehensible, and left without further ado.

MHE.


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