FA_DM.tex

% a4paper = ISO 216 standard. 
% Don't forget to revert to default if you want the US Letter instead.
\documentclass[a4paper,11pt,titlepage,openany, leqno]{book}

%: MATH PACKAGE USED
%\usepackage{graphicx}

\usepackage{amsmath}
\usepackage{
physics, 
amssymb, 
mathrsfs, 
amsthm, 
mathspec, 
fouridx, 
%%stix
%%tensor
theorem, 
tikz
}
\usetikzlibrary{arrows,snakes,backgrounds,patterns,matrix,shapes,fit,calc,shadows,plotmarks}

%\usetikzlibrary{shapes.geometric}
%\usetikzlibrary{arrows.meta,arrows}
%\usepackage{tlatex}
% TEXs LOGOS! 
%\usepackage{dtklogos}

%\usepackage[bottom=3cm,top=2cm]{geometry}
% Metric system, sorry;)
\usepackage[left=3cm,top=3cm,right=3cm,bottom=3cm]{geometry}
%: COLOR
\usepackage{array}
%\usepackage[dvipsnames]{xcolor}
%\usepackage[]{color}
%\usepackage{framed}
\usepackage{colortbl}

%: FOR XELATEX. SKIP IF ERROR MESSAGE
\usepackage{xltxtra,xunicode}
%: for HEVEA- Uncomment before using XeTeX
%\usepackage[utf8]{inputenc}
\usepackage[xetex]{hyperref}
%\usepackage{hyperref}
%\usepackage{listings}
\hypersetup{%
    pdfborder = {0 0 0},
    colorlinks,
    citecolor=red,
    filecolor=green,
    linkcolor=black,
    urlcolor=blue%cyan!50!black!90
}
\defaultfontfeatures{Mapping=tex-text}

% FONTS: PERSONNAL CHOICE- CAN BE CHANGED!
\newfontfamily{\CMUCS}{CMU Classical Serif}
\newfontfamily{\CMU}{CMU Serif}
\newfontfamily{\CMUSS}{CMU Sans Serif}
\newfontfamily{\fw}{CMU Typewriter Text Light}
%\newfontfamily{\Arabic}{Al Bayan}
% On mac OS:
%\newfontfamily{\Didot}{Didot}
% Alternatively, for all Unix systems:
%\newfontfamily{\Didot}{Theano Didot}
%\usepackage{mathspec}
\def\mainfont{CMU Serif}
\setmainfont{\mainfont}

\setmathfont(Latin)[Uppercase=Regular,Lowercase=Regular]{\mainfont}
\setmathfont(Greek)[Uppercase=Regular,Lowercase=Regular]{\mainfont}
\setmathrm{\mainfont}
\setmathbb{\mainfont}
%\setmathit{\mainfont}
\setmathtt{CMU Typewriter Text Light}
%\setmathbf{CMU Serif}


%: TYPOGRAPHIC CONVENTIONS, XETEX
\usepackage{polyglossia}
%\selectbackgroundlanguage[variant=usmax]{english}
\setdefaultlanguage[variant=usmax]{english}

%
%\usepackage{glossaries}
%\makeglossaries


%\newglossaryentry{maths}
%{
%    name=mathematics,
%    description={Mathematics is what mathematicians do}
%}
%: ----------------------------PRIMITIVES------------------------------------- 
\newcommand{\insmall}[1]{\text{\small{#1}}}
% Some acceptable minus sign.
\def\minus{\insmall{-}}

% The field C and the usual subsets R, Q, Z, N. 
\newcommand\usualSet[1]{{\mathbf #1}}
\def\C{\usualSet{C}}
\def\R{\usualSet{R}}
\def\Q{\usualSet{Q}}
\def\Z{\usualSet{Z}}
\def\N{\usualSet{N}}
\def\K{\usualSet{K}}

% "Defined as equals to", alternative to := .
\def\Def{\triangleq}

% The usual scalar field = C, most of the time.
\def\field{\C}

% Counting numbers
\newcommand\counting[1]{#1=1, 2, 3, \dots}
% integers (nonnegative)
\newcommand\integers[1]{#1=0, 1, 2, \dots}
\newcommand{\D}{{\mathscr D}}

% Indices: upper, lower
\newcommand{\up}[1]{^{(#1)}}
\newcommand{\low}[1]{_{#1}}
\newcommand{\upnw}[2]{\fourIdx{#2}{}{}{}#1}
\newcommand{\downsw}[2]{\fourIdx{}{#2}{}{}#1}
\newcommand{\scriptatleft}[3]{\fourIdx{#2}{#3}{}{}#1}
\newcommand{\diagscript}[3]{\fourIdx{#2}{}{}{#3}#1}
%\tensor*[^x]{V}{_k}

% function, relation
\newcommand{\function}[1]{\mathtt{#1}}
\newcommand{\relation}[2]{{#1}_{#2}}
\newcommand{\f}[2]{#1(#2)}


% Sets
%\renewcommand{\notin}{\tiny{\not\in}}
%\renewcommand{\ni}{\small \ni}
\def\contains{\supseteq }
\def\cuts{\cap}
\DeclareMathOperator\cvxhull{co}
\newcommand{\co}[1]{\cvxhull(#1)}
\newcommand{\set}[2]{\{#1: #2\}}
\newcommand{\singleton}[1]{\{#1\}}
\newcommand{\interior}[1]{\overset{\circ}{#1}}
\newcommand{\closure}[1]{\overline{#1}}


% Arithmetics
\newcommand{\ceil}[1]{\lceil #1 \rceilf}
% Analysis
\newcommand\magnitude[1]{\left\lvert\, #1 \,\right\rvert}
\renewcommand{\norm}[2]{\| \,#2 \, \|_{#1}}
\def\weakstar{\text{weak}^\ast\text{-}}
% Topology
\newcommand{\localbase}[1]{\mathscr #1}

%Iverson bracket
\newcommand{\boolean}[1]{\left[\,#1\,\right]}

% limits
\newcommand{\tendsto}[2]{\underset{#1\to #2}{\longrightarrow}}

% Variables
\newcommand{\varit}[1]{\mathit{#1}}
\def\vart{\varit{t}}
%Usual terms
\def\ie{\textit{i.e.} }
\def\eg{\textit{e.g.} }
\def\cf{\textit{cf.\,}}
\def\iif{{\bf iff} }
\def\wlg{{\bf wlg }} % Without loss og generality
\def\then{\Rightarrow}
\def\therefore{\Rightarrow}
\def\since{\Leftarrow}

% Citations
\newcommand{\citehere}[2]{\overset{(#1)}{#2}}
\newcommand{\citeq}[1]{\citehere{#1}{=}}
%\newcomand{\citeineq}[1]{\citehere{#1}{=}}
\newcommand{\citeleq}[1]{\citehere{#1}{\leq}}
\newcommand{\citegeq}[1]{\citehere{#1}{\geq}}
\newcommand{\citeleast}[1]{\citehere{#1}{<}}
\newcommand{\citegreater}[1]{\citehere{#1}{>}}

\newcommand{\citesubset}[1]{\citehere{#1}{\subset}}
\newcommand{\citesupset}[1]{\citehere{#1}{\supseteq }}

\newcommand{\citethen}[1]{\citehere{#1}{\Rightarrow}}
%\newcommand{\citesince}[1]{\citehere{#1}{\Leftarrow}}
\newcommand{\citeresult}[2]{#1 of #2}
\newcommand{\citeresultFA}[1]{\citeresult{#1}{\cite{FA}}}

\newcommand{\citin}[1]{\citehere{#1}{\in}}
% Misc
\newcommand{\underbarwithindex}[2]{\underline{#1}\,\!_{#2}}
\newcommand{\dy}[1]{{\function{dyadic}}(#1)}
\def\ddy{{\function{decay}}}

%--------------END OF PRIMITIVES--------------------------------
\def\ROOT{./}
\def\TITLE{
  Solutions to some exercises from Walter Rudin's \textit{Functional Analysis}
}
\def\EMAIL{}
\def\AUTHOR{gitcordier}

\begin{document}
%\begin{abstract}
%    \input{\ROOT/abstract.tex}
%\end{abstract}
\title{\TITLE}
\author{\AUTHOR}
\date{\today}
\maketitle

% FORMAT ENUMERATION (DEFAULT. OPTIONS: ALPH, ARABIC, ROMAN,…)
\renewcommand{\labelenumi}{$(\textit{\alph{enumi}}\,)$}
% IF LANG = @fr
%\renewcommand{\chaptername}{Chapitre}
%
% CHAPTER  NAME :
\frontmatter
\tableofcontents
%\clearpage

%\printglossary

\input{\ROOT/notations.tex}

\mainmatter
%\part{Content}
\renewcommand{\thechapter}{\arabic{chapter}}
\renewcommand{\thesection}{\arabic{section}}
\renewcommand{\thesubsection}{\arabic{subsection}}
\input{\ROOT/FA_mainmatter.tex}
%\backmatter
%\part{Annex}
%\renewcommand\thechapter{\Alph{chapter}}
%\setcounter{chapter}{1}
%\chapter{Additional results}
%\newcounter{annex}
%\setcounter{annex}{1}
%\renewcommand\thesection{\thechapter.\arabic{annex}}
%\section{Number theory}
%\input{\ROOT/Annex_number_theory.tex}
\bibliographystyle{plain}
\bibliography{bibliography}{}
\addcontentsline{toc}{chapter}{Bibliography}
\end{document}


%Made on \XeTeX