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Re: Ultranet
Posted:
Nov 15, 2012 8:57 AM
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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 mind-bogglingly
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.
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