\documentclass[minion]{homework}
\usepackage{cmacros}
\usepackage{graphicx}
\usepackage{wf}
\usepackage[all,cmtip]{xy}

\doclabel{Math 651: Homework 9}
\docdate{Due: April 8, 2009}
\def\calB{\mathcal{B}}
\begin{document}

\begin{aproblems}
\hproblem Munkres 29.5
\hproblem Munkres 29.6
\hproblem Munkres 29.8
\hproblem Let $X$ be a compact Hausdorff space and let $p\in X$.  Show that
$(X\setminus\{p\})^*$ is homeomorphic to $X$.
\hproblem 
\begin{subproblems}
\item
Show that every manifold is a locally compact Hausdorff space.
\item 
Give an example to show that the one-point compactification of manifold need not be a manifold.
\item Can you find a necessary and sufficient condition on a manifold that will ensure that its one-point compactification is a manifold?  You must state a clear conjecture, but you need not prove it (yet...).
\end{subproblems}
\hproblem Munkres 10.6
\hproblem Munkres 10.7
\end{aproblems}

\end{document}

