\documentclass[12pt,letterpaper]{article}
\usepackage{multicol}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{mathrsfs}
%\usepackage{pstricks, pst-node, pst-plot}

\newcommand{\ds}{\displaystyle}
\newcommand{\bv}{\mathbf}
\newcommand{\lv}{\langle}
\newcommand{\rv}{\rangle}
\newcommand{\R}{{\mathbb{R}}}

\begin{document}


\begin{center}\begin{large}\textbf{Math 131 - Problem Set 5\\
Due Tuesday, Oct 9}\end{large}\end{center}



\pagestyle{empty}

\noindent From Munkres: 18.4, 26.4, 26.6, 26.7, 26.8, 27.2, 27.4 


\begin{enumerate} 

\item Let $X$ be the union of $\R^n$ and one additional point, called $\infty$. Consider the topology $\mathcal{T}$ with basis given by open balls in $\R^n$, plus the sets $$U_r = \{\infty\} \cup \{x \in \R^n \mid |x| > r\}.$$ Show that $X$ is a compact Hausdorff space.

\end{enumerate}

\end{document}