diff --git a/inputs/lecture_15.tex b/inputs/lecture_15.tex
index d408219..38318ea 100644
--- a/inputs/lecture_15.tex
+++ b/inputs/lecture_15.tex
@@ -91,8 +91,8 @@
     Let $X,Y$ be compact metric spaces
     and $\pi\colon (X,T) \to (Y,T)$ a factor map.
     Then $(X,T)$ is an \vocab{isometric extension} 
-    of $(Y,T)$ if there is a real valued $\rho:$
-    defined on the pullback, $\{(x_1,x_2) \in X^2 : \pi(x_1) = \pi(x_2)\}$, % TODO nice notation?
+    of $(Y,T)$ if there is a real valued $\rho$
+    defined on $\{(x_1,x_2) \in X^2 : \pi(x_1) = \pi(x_2)\}$
     such that
     \begin{enumerate}[(a)]
         \item $\rho$ is continuous.