Comments on: Toward Stone Duality: Posets and Meets
https://topologicalmusings.wordpress.com/2008/04/02/toward-stone-duality-posets-and-meets/
Topological MusingsTue, 24 May 2011 16:29:20 +0000
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By: Stephen P. King
https://topologicalmusings.wordpress.com/2008/04/02/toward-stone-duality-posets-and-meets/#comment-1262
Tue, 24 May 2011 16:29:20 +0000http://topologicalmusings.wordpress.com/?p=85#comment-1262Is there any way to define posets within the set of complex numbers such that we can identify the Stone spaces of the posets?
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By: Boolean rings, ultrafilters, and Stone’s representation theorem « Annoying Precision
https://topologicalmusings.wordpress.com/2008/04/02/toward-stone-duality-posets-and-meets/#comment-1047
Tue, 23 Nov 2010 01:46:37 +0000http://topologicalmusings.wordpress.com/?p=85#comment-1047[…] like to introduce them from a different perspective. Some of the topics below are also covered in these posts by Todd […]
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By: Primes and ideals « Annoying Precision
https://topologicalmusings.wordpress.com/2008/04/02/toward-stone-duality-posets-and-meets/#comment-933
Tue, 24 Nov 2009 02:52:19 +0000http://topologicalmusings.wordpress.com/?p=85#comment-933[…] Dedekind accomplished in much the same way) in that both are a special case of thinking about the Yoneda embedding for posets. To think about the reals in terms of the order properties of one embeds in its power […]
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By: ETCS: Internalizing the logic « Todd and Vishal’s blog
https://topologicalmusings.wordpress.com/2008/04/02/toward-stone-duality-posets-and-meets/#comment-482
Thu, 11 Sep 2008 00:10:09 +0000http://topologicalmusings.wordpress.com/?p=85#comment-482[…] the meet operator of an internal meet-semilattice structure on : it is commutative, associative, and idempotent (because that is true of external […]
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By: ZFC and ETCS: Elementary Theory of the Category of Sets « Todd and Vishal’s blog
https://topologicalmusings.wordpress.com/2008/04/02/toward-stone-duality-posets-and-meets/#comment-446
Mon, 01 Sep 2008 08:03:37 +0000http://topologicalmusings.wordpress.com/?p=85#comment-446[…] of off-shoot of the general discussion of ultrafilters I started in connection with the series on Stone duality, and because it seems kind of cool. And I will. But this got finished first, and I thought that it […]
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By: Basic Category Theory, III: Representability, adjoints, and the Yoneda lemma « Todd and Vishal’s blog
https://topologicalmusings.wordpress.com/2008/04/02/toward-stone-duality-posets-and-meets/#comment-362
Sat, 12 Jul 2008 12:23:54 +0000http://topologicalmusings.wordpress.com/?p=85#comment-362[…] to return to today’s topic. Way back when, when we were first discussing posets, most of our examples of posets were of a […]
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By: Basic Category Theory, II « Todd and Vishal’s blog
https://topologicalmusings.wordpress.com/2008/04/02/toward-stone-duality-posets-and-meets/#comment-339
Sun, 29 Jun 2008 14:12:31 +0000http://topologicalmusings.wordpress.com/?p=85#comment-339[…] up to isomorphism by knowing what maps into it look like [they look like pairs of maps ]. In the first lecture in the Stone duality, we stated the Yoneda principle just for posets; now we are generalizing it to […]
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By: Basic category theory, I « Todd and Vishal’s blog
https://topologicalmusings.wordpress.com/2008/04/02/toward-stone-duality-posets-and-meets/#comment-323
Sun, 22 Jun 2008 16:38:07 +0000http://topologicalmusings.wordpress.com/?p=85#comment-323[…] hiatus (sorry about that!), I would like to resume the series on Stone duality. You may recall I started this series by saying that my own point of view on mathematics is strongly informed by category theory, […]
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By: Boolean algebras, Boolean rings, and baby Stone duality « Vishal Lama’s blog
https://topologicalmusings.wordpress.com/2008/04/02/toward-stone-duality-posets-and-meets/#comment-203
Wed, 30 Apr 2008 14:32:42 +0000http://topologicalmusings.wordpress.com/?p=85#comment-203[…] one direction, suppose is a Boolean ring. We know from before that a binary operation on a set that is commutative, associative, unital [has a unit or identity] […]
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By: Lattices and Duality « Vishal Lama’s blog
https://topologicalmusings.wordpress.com/2008/04/02/toward-stone-duality-posets-and-meets/#comment-147
Fri, 04 Apr 2008 16:48:42 +0000http://topologicalmusings.wordpress.com/?p=85#comment-147[…] Calculus by Todd Trimble Tags: inf-lattices, joins, lattices, principle of duality, sup-lattices Previously, on “Stone duality”, we introduced the notions of poset and meet-semilattice […]
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