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Graven Water  
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 More options Nov 7 2009, 2:46 pm
Newsgroups: sci.math
From: p...@grex.org (Graven Water)
Date: Sat, 7 Nov 2009 09:46:04 -0500 (EST)
Local: Sat, Nov 7 2009 2:46 pm
Subject: algebra and analysis
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The complex numbers are algebraically complete.  

And complex analysis has nice theorems that real analysis doesn't have:  
like, if a function is differentiable once, it's differentiable infinitely
many times.  

Are those two things related?

Is something similar true for p-adic analysis - does analysis over the
algebraic completion of the p-adics have nice theorems?  if you could
define a metric on the algebraic completion?

Laura


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