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\documentclass{homework}
\course{Point Set Topology}
\author{Names of Contributors}
\input{preamble}

\begin{document}
\maketitle

\begin{inspiration}
  A quote. \byline{A Person}
\end{inspiration}

\section{Terminology}

\begin{problem}
  What is a \textbf{topological space}?  An \textbf{open set}?  A \textbf{closed set}?
  \label{topological-space}
\end{problem}

\begin{problem}
  What is meant by the \textbf{interior} of a set?
\end{problem}

\begin{problem}
  What is meant by the \textbf{closure} of a set?  Write $\bar{A}$ for the closure of $A$.
\end{problem}

\section{Numericals}

\begin{problem}
  In $\R$ with the standard topology, what is
  $\interior [0,1]$?
\end{problem}

\begin{problem}
  In $\R$ with the standard topology, what is
  $\interior \Q$?
\end{problem}

\section{Exploration}

\begin{problem}
  Describe different topologies on the set $\{ 0, 1 \}$.
\end{problem}

\section{Prove or Disprove and Salvage if Possible (PODASIP)}

\begin{problem}
  The set $X$ is open if and only if $\int X = X$.
\end{problem}


\end{document}