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Re: Ultranet
Posted:
Nov 15, 2012 8:57 AM


On Thu, 15 Nov 2012 01:28:04 0800, William Elliot <marsh@panix.com> wrote:
>What's an example of an universal or ultranet? > >Wikipedia claims that if n:D > X is an ultranet into X and >f:X > Y, then the composition f.n:D > Y is an ultranet into Y. > >I dispute the claim
Did you spend more than a second thinking about it? The proof is completely and utterly mindbogglingly trvial.
It relies on a few deep observations. Say f : X > Y and A is a subset of Y. Say x is an element of x.
(i) Exactly one of the following holds: f(x) is in A, f(x) is not in A.
(ii) f(x) is not in A if and only if f(x) is in Y \ A.
> but knowing of no examples >of ultranets, I'm bankrupt for a counter example.



