From: Peter Selinger <selinger@mathstat.uottawa.ca>
To: categories@mta.ca
Subject: Re: Limit of finite sets
Date: Sat, 31 Jul 2004 08:57:43 -0400 (EDT) [thread overview]
Message-ID: <200407311257.i6VCvhh28559@quasar.mathstat.uottawa.ca> (raw)
In-Reply-To: <32776.62.252.132.5.1091147833.squirrel@mail.maths.gla.ac.uk> from "Tom Leinster" at Jul 30, 2004 01:37:13 AM
This seems to me to be equivalent to Koenig's lemma: every infinite,
finitely branching tree has an infinite branch. The set of vertices is
the disjoint union of all the S_n, and there is an edge from (a,i) to
(b,i+1) if f_i(b)=a. Conversely, let S_n be the set of vertices at
depth n. -- Peter
Tom Leinster wrote:
>
> I've recently come across the following curious little result. I know
> how to prove it and have a use for it, but my question is: can anyone
> supply a wider context or explanation?
>
> The result is that the limit in Set of any diagram
>
> ... ---> S_3 ---> S_2 ---> S_1
>
> of finite nonempty sets is nonempty. Note that finiteness cannot be
> dropped: for instance, take each S_n to be the natural numbers and
> each map to be addition of 1.
>
> Thanks,
> Tom
>
>
>
>
>
*mbx*
42cf5a8f00000000
next prev parent reply other threads:[~2004-07-31 12:57 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2004-07-30 0:37 Tom Leinster
2004-07-30 21:29 ` Prof. Peter Johnstone
2004-07-31 2:00 ` Michael Barr
2004-07-31 12:57 ` Peter Selinger [this message]
2004-07-31 16:09 ` Michael Mislove
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