Re: non-Hausdoff topology

[Vaughan Pratt <pratt@cs.stanford.edu>]

I thought the point of the Lawson topology was to show the opposite:
that the benefits of the Scott topology could be had without having to
broaden topology beyond Hausdorff.

But if one were to so broaden it, wouldn't it be more natural to do so a
la Nachbin and Priestly, with topologized posets?

But if you really like the traditional notion of a topological space in
all its generality, why insist on the closure conditions on open sets
when we know that dropping them gives a category with reasonable
properties, namely extensional Chu(Set,2), further improved to a very
nice category by dropping extensionality, and generalizable to
Chu(Set,K) and yet further to Chu(V,k)?

Vaughan Pratt

On 7/7/2010 1:31 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.
>
> 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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