From a958d5158932ce838fba6f927da5c36b17a56326 Mon Sep 17 00:00:00 2001
From: "juso.koc" <juso.koc@gmail.com>
Date: Fri, 21 Mar 2025 12:06:18 +0000
Subject: [PATCH 1/2] Update on Overleaf.

---
 main.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/main.tex b/main.tex
index 87dadc5..f4591a1 100644
--- a/main.tex
+++ b/main.tex
@@ -233,13 +233,13 @@ code-for-last-col = \color{blue}
 
 \pause
 	\begin{enumerate}
-	    \item We can infer the shape of the universe from its spectrum
+	    \item We can infer the shape of the universe from its spectrum.
 
 \pause
-        \item There are two homogeneous spherical manifolds obtained as $\S^3/\Gamma$ which produce CMB similar to observations
+        \item There are two homogeneous spherical manifolds obtained as $\S^3/\Gamma$ which produce CMB similar to observations.
 
 \pause
-        \item Inhomogeneous spherical spaces exhibit varied behavior of CMB anisotropies
+        \item Inhomogeneous spherical spaces exhibit varied behavior of CMB anisotropies.
 
 \pause
         \item Statistical test results suggest possibilities of finite multi-connected topology

From c52baaf35633b82d601293f2f72bbf2b1ff9df1f Mon Sep 17 00:00:00 2001
From: "juso.koc" <juso.koc@gmail.com>
Date: Fri, 21 Mar 2025 12:06:22 +0000
Subject: [PATCH 2/2] Update on Overleaf.

---
 main.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/main.tex b/main.tex
index f4591a1..049ee47 100644
--- a/main.tex
+++ b/main.tex
@@ -242,7 +242,7 @@ code-for-last-col = \color{blue}
         \item Inhomogeneous spherical spaces exhibit varied behavior of CMB anisotropies.
 
 \pause
-        \item Statistical test results suggest possibilities of finite multi-connected topology
+        \item Statistical test results suggest possibilities of finite multi-connected topology.
 	\end{enumerate}
 \end{frame}