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\textbf{Math 366: Honors Analysis II}
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\textbf{Quiz 1}\quad \textsl{February 2, 2001}

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1. Define
\begin{itemize}
\item[a)] $\limsup$
\item[b)] limit point
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Prove two of the following:

2. $A$ is compact $\Rightarrow$ $A$ is closed and bounded.

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3. $f$ is continuous $\Rightarrow$ $f^{-1}(A)$ is open for all open sets $A$.

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4.  If $f_n$ is continuous and $f_n\to f$ uniformly in $D$, then $f$ is
continuous in $D$.

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