From 006c57fdeb81d97b1ee222d14346e3844df343f5 Mon Sep 17 00:00:00 2001
From: Franciszek Malinka <franciszek.malinka@gmail.com>
Date: Wed, 13 Jul 2022 23:06:05 +0200
Subject: Chyba poprawiony dowod 4.4
---
sections/preliminaries.tex | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
(limited to 'sections/preliminaries.tex')
diff --git a/sections/preliminaries.tex b/sections/preliminaries.tex
index 05aa3ed..2bf254c 100644
--- a/sections/preliminaries.tex
+++ b/sections/preliminaries.tex
@@ -363,7 +363,7 @@
\end{fact}
\begin{proof}
- Suppose that $\eta_(A)$ is an isomorphism for every $A\in\cC$, where
+ Suppose that $\eta_{A}$ is an isomorphism for every $A\in\cC$, where
$\eta_{A}\colon F(A)\to G(A)$ is the morphism of the natural transformation
coresponding to $A$. Then $\eta^{-1}$ is simply given by the morphisms
$\eta^{-1}_A$.
--
cgit v1.2.3
From ae1c456f6467a50427fc485ec5ae163495ea0e52 Mon Sep 17 00:00:00 2001
From: Franciszek Malinka <franciszek.malinka@gmail.com>
Date: Wed, 13 Jul 2022 23:09:49 +0200
Subject: Ortografia
---
sections/preliminaries.tex | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
(limited to 'sections/preliminaries.tex')
diff --git a/sections/preliminaries.tex b/sections/preliminaries.tex
index 2bf254c..0a1b202 100644
--- a/sections/preliminaries.tex
+++ b/sections/preliminaries.tex
@@ -365,7 +365,7 @@
\begin{proof}
Suppose that $\eta_{A}$ is an isomorphism for every $A\in\cC$, where
$\eta_{A}\colon F(A)\to G(A)$ is the morphism of the natural transformation
- coresponding to $A$. Then $\eta^{-1}$ is simply given by the morphisms
+ corresponding to $A$. Then $\eta^{-1}$ is simply given by the morphisms
$\eta^{-1}_A$.
Now assume that $\eta$ is an isomorphism, i.e. $\eta^{-1}\circ\eta = \id_F$.
--
cgit v1.2.3
From 2b830cb2d9c2237fcb7809bab7c64966098ea6fb Mon Sep 17 00:00:00 2001
From: Franciszek Malinka <franciszek.malinka@gmail.com>
Date: Sun, 17 Jul 2022 14:16:41 +0200
Subject: Oby ostatnie poprawki
---
sections/preliminaries.tex | 1 +
1 file changed, 1 insertion(+)
(limited to 'sections/preliminaries.tex')
diff --git a/sections/preliminaries.tex b/sections/preliminaries.tex
index 0a1b202..b27cd69 100644
--- a/sections/preliminaries.tex
+++ b/sections/preliminaries.tex
@@ -76,6 +76,7 @@
\end{definition}
\begin{definition}
+ \label{definition:banach-mazur-game}
Let $X$ be a nonempty topological space and let
$A\subseteq X$. The \emph{Banach-Mazur game of $A$}, denoted as
$G^{\star\star}(A)$ is defined as follows: Players $I$ and
--
cgit v1.2.3