\documentclass[12pt]{article}
\usepackage{amsmath,amsfonts,fullpage}

\def\C{{\mathbb C}}
\def\e{{\mathrm e}}
\def\d{{\mathrm d}}
\def\Ei{\operatorname{Ei}}
\def\N{{\mathbb N}}

\begin{document}

\title{Functional Analysis}
\author{Homework 1}
\date{due February 11, 2009}
\maketitle

\begin{enumerate}
\item Folland, p.\ 118 no.\ 4
\item Folland, p.\ 118 no.\ 10
\item Folland, p.\ 123 no.\ 16

\item Let $X$ be a topological space.  Consider the space $B(X)$ of
  bounded functions $X \to \C$ endowed with the uniform norm\
\[
  \lVert f \rVert_u = \sup_{x \in X} \lvert f(x) \rvert \,.
\]
Prove that $B(X)$ is complete with respect to the uniform metric
$\rho(f,g)=\lVert f-g \rVert_u$.

\end{enumerate}

\end{document}
