From: "Fred E.J. Linton" <fejlinton@usa.net>
To: <categories@mta.ca>
Subject: Re: Sheaf toposes and chain-complete posets
Date: Tue, 28 Jul 2009 00:06:21 -0400 [thread overview]
Message-ID: <E1MVq9I-0000dJ-EI@mailserv.mta.ca> (raw)
On Mon, 27 Jul 2009 05:05:59 PM EDT, Andrej Bauer <andrej.bauer@andrej.com>
asked:
> So what does a chain-complete poset which isn't complete look like?
Take the product of any nonempty discrete poset X with the ordinal 2.
Give Xx2 the "product order" ((x, a) </= (y, b) iff x=y and a </= b).
The only non-singleton nonempty chains are the subsets {x} x 2 .
Clearly each of these is complete, Xx2 is chain-complete, and yet
Xx2 is not at all complete -- not even a semilattice either way.
HTH. Cheers, -- Fred
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next reply other threads:[~2009-07-28 4:06 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2009-07-28 4:06 Fred E.J. Linton [this message]
-- strict thread matches above, loose matches on Subject: below --
2009-07-28 8:35 Sam Staton
2009-07-28 5:44 Andrej Bauer
2009-07-27 12:45 Andrej Bauer
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