Clarify definition for local sections

Signed-off-by: Marcello Seri <marcello.seri@gmail.com>

2c-vectorbdl.tex

@@ -223,7 +223,7 @@ \section{Sections of vector bundles}
 \begin{definition}
   A \emph{section} of a vector bundle $\pi:E \to M$ is a smooth map $S:M \to E$ such that $\pi\circ S = \id_M$. We denote the set of all sections of $E$ by $\Gamma(E)$.
 
-  If, in the definition, $M$ is replaced by $U\subset M$, the section is called \emph{local section}. The set of local sections on $U\subset M$ is denoted $\Gamma(E|_U)$.
+  If, in the definition, $M$ is replaced by $U\subset M$, the section is called \emph{local section}. The set of local sections on $U\subset M$ is denoted $\Gamma(E|_U)$, where $E|_U := \pi^{-1}(U) = \{\eta\in E\;\mid\;\pi(\eta)\in U\} \subset E$ is the vector bundle obtained by restriction of the base of $E$ to $U$.
 \end{definition}
 
 \begin{remark}

aom.tex

@@ -275,7 +275,7 @@ \chapter*{Introduction}
 
 I am extremely grateful to Martijn Kluitenberg for his careful reading of the notes and his invaluable suggestions, comments and corrections, and to Bram Brongers\footnote{You can also have a look at \href{https://fse.studenttheses.ub.rug.nl/25344/}{his bachelor thesis} to learn more about some interesting advanced topics in differential geometry.} for his comments, corrections and the appendices that he contributed to these notes.\medskip
 
-Many thanks also to the following people for their comments and for reporting a number of misprints and corrections: Wojtek Anyszka, Bhavya Bhikha, Huub Bouwkamp, Anna de Bruijn, Daniel Cortlid, Harry Crane, Fionn Donogue, Jordan van Ekelenburg, Brian Elsinga, Hanneke van Harten, Martin Daan van IJcken, Mollie Jagoe Brown, Remko de Jong, Aron Karakai, Hanna Karwowska, Wietze Koops, Henrieke Krijgsheld, Valeriy Malikov, Mar\'ia Diaz Marrero, Aiva Misieviciute, Levi Moes, Nicol\'as Moro, Jard Nijholt, Magnus Petz, Jorian Pruim, Luuk de Ridder, Lisanne Sibma, Marit van Straaten, Bo Tielman, Dave Verweg, Ashwin Vishwakarma, Lars Wieringa, Federico Zadra and Jesse van der Zeijden.
+Many thanks also to the following people for their comments and for reporting a number of misprints and corrections: Wojtek Anyszka, Bhavya Bhikha, Huub Bouwkamp, Anna de Bruijn, Daniel Cortlid, Harry Crane, Fionn Donogue, Jordan van Ekelenburg, Brian Elsinga, Hanneke van Harten, Martin Daan van IJcken, Mollie Jagoe Brown, Remko de Jong, Aron Karakai, Hanna Karwowska, Wietze Koops, Henrieke Krijgsheld, Justin Lin, Valeriy Malikov, Mar\'ia Diaz Marrero, Aiva Misieviciute, Levi Moes, Nicol\'as Moro, Jard Nijholt, Magnus Petz, Jorian Pruim, Luuk de Ridder, Lisanne Sibma, Marit van Straaten, Bo Tielman, Dave Verweg, Ashwin Vishwakarma, Lars Wieringa, Federico Zadra and Jesse van der Zeijden.
 
 \mainmatter