\documentclass[minion]{homework}
\usepackage{cmacros}
\doclabel{Math F651: Homework 4}
\docdate{Due: February 16, 2011}
\begin{document}
\begin{aproblems}

    \hproblem Finish the proof from class that a space is Hausdorff if and only if sequences have unique limits.
    We proved that in Hausdorff spaces, limits are unique.  Prove the other direction, and go after a short proof.

    \hproblem Suppose $A\subseteq X$.  Show $\overline{A^c} = ({\rm Int}(A))^c$.
    
    \hproblem Munkres 17.6

    \hproblem Munkres 17.19
    
    \hproblem Munkres 17.14
    
    \hproblem 16.4
    
    \hproblem Let $X=\{ x\in\Reals^2: 1<|x|<2\}$.  Let $Y=\{(a,b,c)\in\Reals^3: a^2+b^2=1 \}$.
    Show that $X$ and $Y$ (each with the subspace topology) are homeomorphic.
    \Hint You might want to show that $(1,2)$ is homeomorphic to $\Reals$ separately.

    \hproblem 18.4
    
    \hproblem 18.10

\end{aproblems}

\end{document}