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Diffstat (limited to 'sections/preliminaries.tex')
| -rw-r--r-- | sections/preliminaries.tex | 5 |
1 files changed, 3 insertions, 2 deletions
diff --git a/sections/preliminaries.tex b/sections/preliminaries.tex index 05aa3ed..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 @@ -363,9 +364,9 @@ \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 + corresponding to $A$. Then $\eta^{-1}$ is simply given by the morphisms $\eta^{-1}_A$. Now assume that $\eta$ is an isomorphism, i.e. $\eta^{-1}\circ\eta = \id_F$. |