From fa334cef8c04e50a45b366a3427db18e638fc992 Mon Sep 17 00:00:00 2001
From: Franciszek Malinka <franciszek.malinka@gmail.com>
Date: Sun, 10 Jul 2022 20:24:41 +0200
Subject: Capitalised words before \ref

---
 sections/preliminaries.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'sections/preliminaries.tex')

diff --git a/sections/preliminaries.tex b/sections/preliminaries.tex
index 266845c..82e64b4 100644
--- a/sections/preliminaries.tex
+++ b/sections/preliminaries.tex
@@ -85,7 +85,7 @@
     $\bigcap_{n}V_n \subseteq A$.  
   \end{definition}
 
-  There is an important theorem \ref{theorem:banach_mazur_thm} on the 
+  There is an important Theorem \ref{theorem:banach_mazur_thm} on the 
   Banach-Mazur game: $A$ is comeagre if and only if $\textit{II}$ can always
   choose sets $V_0, V_1, \ldots$ such that it wins. Before we prove it we need 
   to define notions necessary to formalise and prove the theorem.
@@ -254,7 +254,7 @@
 
   Now we can move to the proof of the Banach-Mazur theorem.
 
-  \begin{proof}[Proof of theorem \ref{theorem:banach_mazur_thm}]
+  \begin{proof}[Proof of Theorem \ref{theorem:banach_mazur_thm}]
     $\Rightarrow$: Let $(A_n)$ be a sequence of dense open sets with
     $\bigcap_n A_n\subseteq A$.  The simply $\textit{II}$ plays $V_n
     = U_n\cap A_n$, which is nonempty by the denseness of $A_n$.
@@ -277,7 +277,7 @@
   \begin{corollary} 
     \label{corollary:banach-mazur-basis} 
     If we add a constraint to the Banach-Mazur game such that players can only 
-    choose basic open sets, then the theorem \ref{theorem:banach_mazur_thm} 
+    choose basic open sets, then the Theorem \ref{theorem:banach_mazur_thm} 
     still suffices.  
   \end{corollary}
 
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