\documentclass[minion]{homework}
\usepackage{cmacros}
%\usepackage{times}

\doclabel{Math 651: Homework 3}
\docdate{Due: February 13, 2009}
\def\calB{\mathcal{B}}
\begin{document}

\begin{aproblems}

\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 $Y$ (with the subspace topology) are homeomorphic.
\Hint You might want to show that $(1,2)$ is homeomorphic to $\Reals$ separately.

\hproblem Read \textsection 14. Let $I$ be the interval $(0,1)$.  Let $X$ be the set $I\times I$
with the topology inherited from $\Reals^2$ with the order topology,
and let $Y$ be the same set with the usual metric topology. Determine if either
of the identity maps $X\ra Y$ or $Y\ra X$ are continuous.

\hproblem Munkres 16.9

\hproblem Munkres 16.4

\hproblem Munkres 18.4 (See the definition of {\it imbedding} at the bottom of page 105.)

\hproblem Munkres 18.10

\hproblem Show that $S^1\times\Reals$ is homeomorphic to the space $Y$ of problem 1.

\end{aproblems}

\end{document}
