diff --git a/src/topology/main/compact.tex b/src/topology/main/compact.tex
index db05182..8cf2c96 100644
--- a/src/topology/main/compact.tex
+++ b/src/topology/main/compact.tex
@@ -19,9 +19,7 @@
     U_J = \bigcup_{j \in J}E_j^c
     \]
 
-    then $U_J \subset X$ is open. For any $J, J' \subset I$, $U_J \cup U_{J'} = U_{J \cup J'}$.
-
-    Suppose for contradiction that $\bigcap_{i \in I}E_i = \emptyset$, then
+    then $U_J \subset X$ is open. Suppose for contradiction that $\bigcap_{i \in I}E_i = \emptyset$, then
     \[
     \mathbf{U} = \bracs{U_J|J \subset I \text{ finite}}
     \]