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\textbf{Math 366: Honors Analysis II}
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\textbf{Quiz 3}\quad \textsl{March 2, 2001}

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1. Define:

a) metric space

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b) normed vector space

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2.  a) State the Cauchy-Schwartz Inequality.

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b) Use the Cauchy-Schwartz Inequality to show that an inner product space
has a natural norm.

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Prove two of the following:

4. Let $M$ be a metric space. Prove that $A$ is closed if and only if $A^c$
is open.

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5. $C[a,b]$ with the sup-norm is a complete metric metric space.

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6. Prove that if $A$ is a compact subset of a metric space $M$, then every
sequence $\{x_n\}\subset M$ has a convergent subsequence.

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