% Author: Michael Starbird, Francis Edward Su
% Title:
\documentclass[11pt]{book}
%\documentclass[11pt, titlepage]{book}


%-------------------------CONFIGURE-----------------------------------------------------------------------------
%   USE ONLY ONE OF THE FOLLOWING TWO LINES

% UNCOMMENT THE NEXT LINE IF YOU WANT ONE THEOREM PER PAGE
 %\newcommand{\oneperpage}{\newpage}

% UNCOMMENT THE NEXT LINE IF YOU WANT ALL THEOREMS TOGETHER
 \newcommand{\oneperpage}{}

%-----------------------------------------------------------------------------------------------------------------------


%\usepackage{endnotes}

%makes hints/solutions
\usepackage{answers}
\Newassociation{inst}{Instructor}{ans}
\Newassociation{hint}{Hint}{ans}
\Newassociation{sol}{Solution}{ans}

\usepackage{dutchcal}% fonts
\usepackage{amsmath, amssymb,latexsym, amsthm, amsfonts, amscd}
\usepackage{verbatim}
\usepackage{epsfig}
\usepackage{makeidx}

%\usepackage{graphics}
\usepackage{graphicx}
\usepackage[all,cmtip]{xy}


%F
\usepackage{palatino}


\usepackage{fullpage}
%\usepackage{geometry}
%\setlength{\textwidth}{6in}
%\setlength{\textheight}{8.5in}
%\setlength{\topmargin}{-0.25in}
%\setlength{\oddsidemargin}{0.2in}
%\setlength{\evensidemargin}{0.2in}
%\setlength{\headsep}{.3in}

%\pagestyle{headings}


%\usepackage{fancyhdr}
%\pagestyle{fancy}
%\renewcommand{\chaptermark}[1]{%
%\markboth{\thechapter.\ #1}{}}
%\renewcommand{\chaptermark}[1]{\markright{#1}{}}
%\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}
%\renewcommand{\chaptermark}[1]{\markboth{}{}}
\renewcommand{\sectionmark}[1]{\markboth{Topology Through Inquiry - DRAFT}{Topology Through Inquiry - DRAFT}}

%\chead{\chaptermark}
%\lhead{}
%\rhead{}
%\cfoot{\thepage}
%\renewcommand{\headrulewidth}{0.4pt}
%\renewcommand{\footrulewidth}{0.4pt}




\newtheorem{thm}{Theorem}[chapter]
\newtheorem*{thm*}{Theorem}%[chapter]
%\newtheorem{*thm}[thm]{*Theorem}

%\newtheorem{thm-d}[thm]{$\diamond$ Theorem}   % notation for theorems that are optional?
%\newtheorem{thm-dd}[thm]{Theorem $\diamond$ } % notation for theorems that are optional?

%\newtheorem{THM*}{Theorem}
%\newtheorem*{thma}{Theorem}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{lemma}[thm]{Lemma}
%\newtheorem{prop}[thm]{Proposition}
\newtheorem{pro}[thm]{Proposition}
\newtheorem{scholium}[thm]{Scholium}

\newtheorem{question}[thm]{Question}%
\newtheorem{exercise}[thm]{Exercise}  % The numbering and style of exercises and theorem should be the same.
%F
\newtheorem{statement}[thm]{True/False Statement}
%\newtheorem{fact}[thm]{Fact}

\newtheorem{normlemma}[thm]{Normality Lemma}
\newtheorem{HBthm}[thm]{Heine-Borel Theorem}
\newtheorem{ASthm}[thm]{Alexander Subbasis Theorem}
\newtheorem{urysohn}[thm]{Urysohn's Lemma}
\newtheorem{Tietze}[thm]{Tietze Extension Theorem}
%\newtheorem{Tych}[thm]{Tychonoff Theorem}
%\newtheorem{mthm}[thm]{Metatheorem}
\newtheorem{LebesgueNumThm}[thm]{Lebesgue Number Theorem}
\newtheorem{UrysohnMetrization}[thm]{Urysohn's Metrization Theorem}
\newtheorem{Bing}[thm]{The Bing Metrization Theorem}
\newtheorem{Nagata-Smirnov}[thm]{The Nagata-Smirnov Metrization Theorem}



\newtheorem{Cantor's Theorem}[thm]{Cantor's Theorem}
\newtheorem{Cantor's Power Set Theorem}[thm]{Cantor's Power Set Theorem}
\newtheorem{Tychonoff's Theorem}[thm]{Tychonoff's Theorem}
%\newtheorem{The Pasting Lemma}[thm]{The Pasting Lemma}


\newtheorem*{Zorn}{Zorn's Lemma}
\newtheorem*{AxChoice}{Axiom of Choice}
\newtheorem*{WellOrPrin}{Well-Ordering Principle}
\newtheorem*{Continuum}{Continuum Hypothesis}
%F
%\newtheorem*{Axiom}{The Axiom of Choice}
%\newtheorem*{Well}{The Well-Ordering Theorem}



\theoremstyle{remark}
\newtheorem{ax}{Axiom}
%\newtheorem{pr}[thm]{Problem}
\newtheorem*{example}{Example}
\newtheorem*{examples}{Examples}

%\newtheorem*{learning}{Effective Learning Principle}
\newenvironment{learning}[1][\unskip]
    {
    \smallskip
    \begin{center}
    \begin{tabular}{|p{0.9\textwidth}|}
    \hline\\
    \textbf{Effective Thinking Principle.} \textit{#1.}
    }
    { 
    \\\\
    %\\\\
    \hline
    \end{tabular} 
    \end{center}
    \smallskip
    }

\newtheorem*{defn}{Definition}
\newtheorem{remark}{Remark}
%\newtheorem{revthm}[thm]{Review Theorem}

\newtheorem*{dfn}{Definition} %F 
\newtheorem*{dfns}{Definitions}
\newtheorem*{note}{Note}
\newtheorem*{rem}{Remark}
\newtheorem*{notation}{Notation}



\numberwithin{equation}{section}


\newcommand{\ignore}[1]{}
% alter this if you want different headings
%\pagestyle{myheadings}
%\markright{Math 147 (Su): Topology}

\newcommand{\opt}[1]{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% COMMENT OUT THE NEXT TWO LINES IF YOU DON'T WANT SOLUTIONS
%{\small \begin{minipage}{1in} \quad \end{minipage}
%\begin{minipage}{5in} #1 \end{minipage}} \\
}

\newcommand{\added}[1]{#1}
\newcommand{\Cl}[1]{\overline{#1}}


\newcommand{\nibf}{\noindent \textbf}
\newcommand{\niit}{\noindent \textit}


\newcommand{\HH}{\mathsf{H}}
\newcommand{\ZZ}{\mathsf{Z}}
\newcommand{\CC}{\mathsf{C}}
\newcommand{\BB}{\mathsf{B}}

\DeclareMathOperator{\sd}{\mathsf{sd}}
%\def\sd{\mathop{\mathsf{sd}}\nolimits}
\DeclareMathOperator{\sdop}{\mathsf{SD}}
%\def\sdop{\mathop{\mathsf{SD}}\nolimits}
\DeclareMathOperator{\cone}{\mathsf{Cone}}
\DeclareMathOperator{\coneop}{\mathrm{Cone}}
%\newcommand{\cone}{\mathsf{Cone}}
\renewcommand{\emptyset}{\varnothing}
\DeclareMathOperator{\idop}{\mathsf{id}}
\DeclareMathOperator{\tr}{\mathsf{Tr}}
\DeclareMathOperator{\st}{St}


\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\D}{\mathbb{D}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\PP}{\mathbb{R}\mathrm{P}}
\newcommand{\Sph}{\mathbb{S}}
\newcommand{\T}{\mathbb{T}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\K}{\mathbb{K}}
%\newcommand{\B}{\mathbb{B}}
%\newcommand{\A}{\mathbb{A}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\E}{\mathbb{E^{\infty}}}

\newcommand{\RLL}{\R_{\mathrm{LL}}}
\newcommand{\Hbub}{\mathbb{H}_\mathrm{bub}}

\newcommand{\wt}{\widetilde}
%\newcommand{\bs}{\backslash}

%\newcommand{\beq}{\begin{equation}}
%\newcommand{\eeq}{\end{equation}}
%\newcommand{\bea}{\begin{eqnarray}}
%\newcommand{\eea}{\end{eqnarray}}
\newcommand{\bi}{\begin{itemize}}
\newcommand{\ei}{\end{itemize}}
\newcommand{\be}{\begin{enumerate}}
\newcommand{\ee}{\end{enumerate}}

%\renewcommand{\baselinestretch}{2}
\renewcommand{\arraystretch}{1}

\newcommand{\no}{\noindent}
\newcommand{\ol}{\overline}
\newcommand{\ul}{\underline}
\newcommand{\al}{\alpha}

%F
\newcommand{\ff}{($\Rightarrow$) }
\newcommand{\bk}{($\Leftarrow$) }
\newcommand{\key}{{\bf KEY IDEA: }}
\newcommand{\keypoint}{{\bf KEY POINT: }}


\def\dim{\mathop{\rm dim}\nolimits}
\def\image{\mathop{\rm Im}\nolimits}  
\def\interior{\mathop{\rm Int}\nolimits}
\def\kernel{\mathop{\rm Ker}\nolimits}
\def\cokernel{\mathop{\rm Coker}\nolimits}
\def\bd{\mathop{\rm Bd}\nolimits}
\def\ext{\mathop{\rm Ext}\nolimits}
\def\num{\mathop{\#}\limits}
\def\cl{\mathop{\rm Cl}\nolimits}
\def\lub{\mathop{\rm lub}\nolimits}


\newcommand{\relation}{\leq}
\newcommand{\cantor}{X_{C}}
\newcommand{\varep}{\varepsilon}
\newcommand{\np}{\vfill\eject} 
\newcommand{\vup}{\vspace{-.08in}} 


%F
\newcommand{\Tau}{{\mathcal T}}
\newcommand{\B}{{\mathcal B}}
\newcommand{\eps}{\epsilon}
%\newcommand{\topspace}{topological space $(X,\Tau)$}


% changes \marginpar command to make text smaller

\setlength{\marginparwidth}{2cm}
\let\oldmarginpar\marginpar
\renewcommand\marginpar[1]{\-\oldmarginpar[\raggedleft\footnotesize #1]%
{\raggedright\footnotesize #1}}

% make command \marginnote (comment first line, uncomment 2nd line if you don't want margin notes)
\newcommand{\marginnote}[1]{\marginpar{#1}}
%\newcommand{\marginnote}[1]{}


%makes a star section (e.g. for advanced sections)

\newcommand{\starsection}[1]{\addtocounter{section}{1}%
\addcontentsline{toc}{section}{*\thesection\hspace{1em}#1}%
{\vspace{1.5em}\par\noindent\bfseries\Large *\thesection\hspace{0.5em} #1}\par\vspace{0em}\noindent}

%makes index
\makeindex

%------------------document begins-----------------------

\begin{document}

%%solutions
\Opensolutionfile{ans}


        \baselineskip=.25in

\title{Topology Through Inquiry\\
\opt{
(with Solutions)
}
}

\author{Michael Starbird and Francis Edward Su}
%\date{Math 147\\ Harvey Mudd College\\ January 19, 2005}
\maketitle
\vfill
\copyright Michael Starbird and Francis Edward Su, 2004-2018. All rights reserved.

\bigskip
This is a DRAFT.  DO NOT DISTRIBUTE without explicit permission of the authors.
%\begin{abstract}
%\end{abstract}

\tableofcontents


%\setcounter{chapter}{0}  
%\setcounter{chapter}{-1}  

%\include{-preface-thms}
%\include{0-introbook}
%\include{0-intro-thms}

\part{Point-Set Topology}

\include{1-cardinality-thms}
\include{2-generaltopology-thms}
\include{3-newspaces-thms}
\include{4-separation-thms}
\include{5-countablefeatures-thms}
\include{6-compactness-thms}
\include{7-continuity-thms}
\include{8-connectedness-thms}
\include{9-metricspaces-thms}


%\part{Transition from Point-Set Topology to Algebraic and Geometric Topology}



%--------------------------------------------------------

%\include{francis-alg-top}


\part{Algebraic and Geometric Topology}

\setcounter{chapter}{10}  

%\include{10-reflection-part1-thms}
\include{11-classification-2mflds-thms}
\include{12-fundamentalgroup-thms}
\include{13-coveringspaces-thms}
\include{14-complexes-manifolds-thms}
\include{15-Z2homology-thms}
\include{16-Z2applications-thms}
\include{17-Zhomology-thms}
\include{18-singular-homology-thms}
%\include{more-homology}
\include{19-reflection-part2-thms}


%\include{old-homology-stuff}

%\include{ham}

\appendix
\include{20-appendix-thms}
%\include{more-homology}

%solutions
%
%\Closesolutionfile{ans}
%\chapter{Hints for Selected Theorems}
%\input{ans}


\printindex


\end{document}















