# HG changeset patch # User Scott Morrison # Date 1312767194 25200 # Node ID 9020b09ddc639b783952e662935e087267d388a8 # Parent daa522adb4881888b2cd21c74f24c2586c11a978 minor: fixing common refinement example diff -r daa522adb488 -r 9020b09ddc63 text/a_inf_blob.tex --- a/text/a_inf_blob.tex Fri Aug 05 12:27:11 2011 -0600 +++ b/text/a_inf_blob.tex Sun Aug 07 18:33:14 2011 -0700 @@ -119,7 +119,7 @@ the case. (Consider the $x$-axis and the graph of $y = e^{-1/x^2} \sin(1/x)$ in $\r^2$.) However, we {\it can} find another decomposition $L$ such that $L$ shares common -refinements with both $K$ and $K'$. (For instance, in the example above, $L$ can be the graph of $y=x^2+1$.) +refinements with both $K$ and $K'$. (For instance, in the example above, $L$ can be the graph of $y=x^2-1$.) This follows from Axiom \ref{axiom:vcones}, which in turn follows from the splitting axiom for the system of fields $\cE$. Let $KL$ and $K'L$ denote these two refinements.