replace \fG

2021_Algebra_I.tex

@@ -2329,13 +2329,13 @@ If $P_e $ with $e < d$ was $\neq 0$, it could not be a multiple of $P$ contradic
 
 \subsubsection{Examples of sheaves}
 \begin{example}
-    Let $G$ be a set and let $\fG(U)$ be the set of arbitrary maps $U \xrightarrow{f} G$. We put $r_{U,V}(f) = f\defon{V}$.
+    Let $G$ be a set and let $\mathfrak{G}(U)$ be the set of arbitrary maps $U \xrightarrow{f} G$. We put $r_{U,V}(f) = f\defon{V}$.
     It is easy to see that this defines a sheaf.
-    If $\cdot $ is a group operation on $G$, then $(f\cdot g)(x) \coloneqq f(x)\cdot g(x)$ defines the structure of a sheaf of group on $\fG$.
-    Similarly, a ring structure on $G$ can be used to define the structure of a sheaf of rings on  $\fG$.
+    If $\cdot $ is a group operation on $G$, then $(f\cdot g)(x) \coloneqq f(x)\cdot g(x)$ defines the structure of a sheaf of group on $\mathfrak{G}$.
+    Similarly, a ring structure on $G$ can be used to define the structure of a sheaf of rings on  $\mathfrak{G}$.
 \end{example}
 \begin{example}
-    If in the previous example $G$ carries a topology and $\mathcal{G}(U) \subseteq \fG(U)$ is the subset (subring, subgroup) of continuous functions $U \xrightarrow{f} G$, then $\mathcal{G}$ is a subsheaf of  $\fG$, called the sheaf of continuous $G$-valued functions on (open subsets of) $X$.
+    If in the previous example $G$ carries a topology and $\mathcal{G}(U) \subseteq \mathfrak{G}(U)$ is the subset (subring, subgroup) of continuous functions $U \xrightarrow{f} G$, then $\mathcal{G}$ is a subsheaf of  $\mathfrak{G}$, called the sheaf of continuous $G$-valued functions on (open subsets of) $X$.
 \end{example}
 
 \begin{example}