Re: the magic mystery tourantiquitykinNovember 23 2003, 02:58:47 UTC
I swear, every time I see your name I think of that strongbad email from "seb, the lodge." it's awesome. because after that I inadvertently read the rest of your comment as strongbad talking.
Re: :)<-<|:-E:*()D*spacegoddessNovember 24 2003, 08:47:53 UTC
Yeah, yeah. AYE! Picture perfect. I am painfully awesome, because I am just so damn awesome that it hurts. And, uh, I have guns, too. And empty turtle aquariums to launch at the programmers who have the secret cheat codes to life. ;K3
i heard this song on the radio.antiquitykinNovember 24 2003, 19:17:50 UTC
Spectral Decomposition of Ultrametric Spaces and Topos Theory We consider categories METR and METRc of metric spaces (of diameter <= c) and non-expanding maps as well as their subcategories ULTRAMETR and ULTRAMETRc of ultrametric spaces and the same maps. Given a family of ultrametric spaces, we prove that sums and products, equalizer and co-equalizer, pull-back and push-out, limits of direct and inverse spectra, if exist, are ultrametric. A product and a limit of inverse spectrum of complete metric spaces are complete. A space (X,d) is uniformly discrete if d(x,y) >= \epsilon > 0 'for all' x, y \in X. This is necessarily complete. Theorem. Every complete ultrametric space is isometric to a limit of a countable inverse spectrum of uniformly discrete ultrametric spaces (and vise versa) (see [1]). Corollary 1. Every compact ultrametric space is isometric to a limit of inverse sequence of skeletons of finite dimensional isosceles simplexes lying in Euclidean spaces (see [2]). Corollary 2. Category ULTRAMETR is a quasi-topos.
Comments 13
What now your jewish?
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I was beyond foozled last night. thought didn't even seem like a good idea before 2am.
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see any pretty lights?
cause the last time i did shrooms, i was in a vangoh painting.
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me toooooooo!
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seb
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yeah. a bit stolen from me because i am so terribly painfully awesome.
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We consider categories METR and METRc of metric spaces (of diameter <= c) and non-expanding maps as well as their subcategories ULTRAMETR and ULTRAMETRc of ultrametric spaces and the same maps. Given a family of ultrametric spaces, we prove that sums and products, equalizer and co-equalizer, pull-back and push-out, limits of direct and inverse spectra, if exist, are ultrametric. A product and a limit of inverse spectrum of complete metric spaces are complete. A space (X,d) is uniformly discrete if d(x,y) >= \epsilon > 0 'for all' x, y \in X. This is necessarily complete.
Theorem. Every complete ultrametric space is isometric to a limit of a countable inverse spectrum of uniformly discrete ultrametric spaces (and vise versa) (see [1]).
Corollary 1. Every compact ultrametric space is isometric to a limit of inverse sequence of skeletons of finite dimensional isosceles simplexes lying in Euclidean spaces (see [2]).
Corollary 2. Category ULTRAMETR is a quasi-topos.
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