🚀 go-pugleaf

In article <BEVAN.91Jun16180108@panda.cs.man.ac.uk> bevan@cs.man.ac.uk (Stephen J Bevan) writes:
>
>Anyway, my problem (for today :-) is that I can't think of a function
>on a CPO (complete partial order) that is monotonic but is _not_
>continuous.  

You can't find such an example unless your cpo has infinite ascending
chains. If it has, the example is straightforward. Consider N (natural
numbers) as a chain and add the top element T. Now, the function
f: N union {T} ---> {0,1}  (where 0 < 1, of course) given by
f(n) = 0 if n \in N and f(T) = 1 is monotone (obvious) but not
continuous: f(supN) = f(T) = 1, but supf(n) = 0.



>So, can anybody help me with my (hopefully simple) question and also
>point me at a book/report/paper that explains these sorts of things
>and actually has some examples to go along with the (dry) definitions!

I think Gunter and Scott's recent survey in the Handbook on theoretical
comp sci has this example or somewhat similar.


>
>Stephen J. Bevan			bevan@cs.man.ac.uk
>
>PS. Just in case anybody is wondering :- this is not home/course work

Leonid
libkin@saul.cis.upenn.edu