From 8ff3cadebd6762f0497362d12d84b62e10b9a5e5 Mon Sep 17 00:00:00 2001
From: Josia Pietsch <git@jrpie.de>
Date: Fri, 5 Jan 2024 17:43:25 +0100
Subject: [PATCH] small fix

---
 inputs/lecture_17.tex | 2 +-
 inputs/lecture_18.tex | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/inputs/lecture_17.tex b/inputs/lecture_17.tex
index 16d5e8b..c7f8775 100644
--- a/inputs/lecture_17.tex
+++ b/inputs/lecture_17.tex
@@ -23,7 +23,7 @@ $X^{X}$ is a compact Hausdorff space.
         \item $X^X \ni f \mapsto f \circ f_0$
             is continuous:
 
-            Consider $\{f : f f_0 \in U_{\epsilon}(x,y)\}$.
+            Consider $\{f : f \circ f_0 \in U_{\epsilon}(x,y)\}$.
             We have $ff_0 \in U_{\epsilon}(x,y)$
             iff $f \in U_\epsilon(x,f_0(y))$.
         \item Fix $x_0 \in X$.
diff --git a/inputs/lecture_18.tex b/inputs/lecture_18.tex
index 9acb47f..4a21148 100644
--- a/inputs/lecture_18.tex
+++ b/inputs/lecture_18.tex
@@ -108,7 +108,7 @@ This will follow from the following lemma:
     is continuous.
     Since $T_n$ is compact,
     we have that $\{(x,t) \mapsto tx : t \in T_n\}$
-    is equicontinuous for all $n$.
+    is equicontinuous.
     So there is $\epsilon > 0$ such that
     $d(x_1,x_2) < \epsilon \implies d(tx_1, tx_2) < a -b$
     for all $t \in T_n$.