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\date{Due Tuesday, 3/12}
\title{Math 104 Homework 7 (Vaintrob)}
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\section{Reading Exercise 1}
Read the proof of theorem 18.5: show that the condition ``$g(J)$ is an interval'' is necessary: find a strictly increasing function $g$ which does not have a continuous inverse. Where is it used in the proof?

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\section{15.4}

\section{17.4}
\section{17.8}
\section{17.9} (a, b)

\section{18.2}
\section{18.5, 18.7}
\section{18.10}
\section{Extra credit.} Prove that our definition of continuity (either one) is equivalent to the following definition:
``a function $f(x)$ is continuous if and only if $f^{-1}(U)$ is open for any open $U\subset \R$''. Here $f^{-1}(U)$ is the set of all elements $\{r\in \R\mid f(r)\in U\}.$

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