From 006c57fdeb81d97b1ee222d14346e3844df343f5 Mon Sep 17 00:00:00 2001 From: Franciszek Malinka 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 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 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